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Longer titles found: Non-associative algebra (view), Commutant-associative algebra (view), Free product of associative algebras (view), Homotopy associative algebra (view)

searching for Associative algebra 73 found (296 total)

alternate case: associative algebra

Supercommutative algebra (303 words) [view diff] no match in snippet view article find links to article

In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we
Moufang polygon (1,356 words) [view diff] no match in snippet view article find links to article
In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of rank
Jacobi identity (1,092 words) [view diff] exact match in snippet view article find links to article
That is easily checked by computation. More generally, if A is an associative algebra and V is a subspace of A that is closed under the bracket operation:
Cancellation property (695 words) [view diff] no match in snippet view article find links to article
In mathematics, the notion of cancellativity (or cancellability) is a generalization of the notion of invertibility. An element a in a magma (M, ∗) has
Monster vertex algebra (200 words) [view diff] no match in snippet view article find links to article
The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky
Hyperbolic quaternion (2,024 words) [view diff] exact match in snippet view article find links to article
In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q=a+bi+cj+dk,a,b
Moufang loop (1,668 words) [view diff] no match in snippet view article find links to article
In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops
CH-quasigroup (56 words) [view diff] no match in snippet view article find links to article
In mathematics, a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian
Admissible algebra (61 words) [view diff] no match in snippet view article find links to article
In mathematics, an admissible algebra is a (possibly non-associative) commutative algebra whose enveloping Lie algebra of derivations splits into the sum
Bol loop (799 words) [view diff] no match in snippet view article find links to article
In mathematics and abstract algebra, a Bol loop is an algebraic structure generalizing the notion of group. Bol loops are named for the Dutch mathematician
Quasifield (805 words) [view diff] no match in snippet view article find links to article
In mathematics, a quasifield is an algebraic structure (Q,+,⋅){\displaystyle (Q,+,\cdot )} where +{\displaystyle +} and ⋅{\displaystyle \cdot } are binary
Isotopy of loops (825 words) [view diff] no match in snippet view article find links to article
In the mathematical field of abstract algebra, isotopy is an equivalence relation used to classify the algebraic notion of loop. Isotopy for loops and
Latin square (3,514 words) [view diff] no match in snippet view article find links to article
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row
Heap (mathematics) (1,453 words) [view diff] no match in snippet view article
In abstract algebra, a semiheap is an algebraic structure consisting of a non-empty set H with a ternary operation denoted [x,y,z]∈H{\displaystyle [x,y
Lie conformal algebra (420 words) [view diff] no match in snippet view article find links to article
A Lie conformal algebra is in some sense a generalization of a Lie algebra in that it too is a "Lie algebra," though in a different pseudo-tensor category
Griess algebra (169 words) [view diff] exact match in snippet view article find links to article
In mathematics, the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 that has the Monster group M as
Biracks and biquandles (916 words) [view diff] no match in snippet view article find links to article
In mathematics, biquandles and biracks are sets with binary operations that generalize quandles and racks. Biquandles take, in the theory of virtual knots
Gyrovector space (3,905 words) [view diff] case mismatch in snippet view article find links to article
gyrogroup L.V. Sabinin, Larissa Sbitneva, I.P. Shestakov (2006), "Non-associative Algebra and Its Applications", CRC Press,ISBN 0-8247-2669-3, ISBN 978-0-8247-2669-0
Medial magma (850 words) [view diff] no match in snippet view article find links to article
In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) that satisfies the identity (x •
Small Latin squares and quasigroups (3,258 words) [view diff] no match in snippet view article find links to article
Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic. The
Jacobson–Bourbaki theorem (434 words) [view diff] exact match in snippet view article find links to article
sub division rings of a division ring and some subalgebras of an associative algebra. The Jacobson–Bourbaki theorem implies both the usual Galois correspondence
Cyclotomic identity (269 words) [view diff] exact match in snippet view article find links to article
the cyclotomic identity is the generating function for the free associative algebra on α generators, and the right hand side is the generating function
Idempotence (2,877 words) [view diff] exact match in snippet view article find links to article
"Linear associative algebra". American Journal of Mathematics. 4 (1): 97–229. See p. 104. Reprinted: Peirce, Benjamin (1882). Linear Associative Algebra (PDF)
Commutator collecting process (470 words) [view diff] exact match in snippet view article find links to article
be generalized to define a totally ordered subset of a free non-associative algebra, that is, a free magma; this subset is called the Hall set. Members
Nilpotent (1,145 words) [view diff] exact match in snippet view article find links to article
is an important example in physics. As linear operators form an associative algebra and thus a ring, this is a special case of the initial definition
Octonion algebra (809 words) [view diff] exact match in snippet view article find links to article
dimension 8 over F. In other words, it is a 8-dimensional unital non-associative algebra A over F with a non-degenerate quadratic form N (called the norm
Quadratic Jordan algebra (5,195 words) [view diff] exact match in snippet view article find links to article
field: A is central if its centroid is just K. If A is a unital associative algebra over K with multiplication × then a quadratic map Q can be defined
Vertex operator algebra (8,548 words) [view diff] no match in snippet view article find links to article
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Hall word (3,144 words) [view diff] exact match in snippet view article find links to article
set. This set is a particular totally ordered subset of a free non-associative algebra, that is, a free magma. In this form, the Hall trees provide a basis
Hochschild homology (3,119 words) [view diff] exact match in snippet view article find links to article
groups and the homology ring HH∗(A){\displaystyle HH_{*}(A)} for an associative algebra A{\displaystyle A}. For the case of commutative algebras, there are
Algebra bundle (194 words) [view diff] exact match in snippet view article find links to article
MR 0336651. Chidambara, C.; Kiranagi, B. S. (1994), "On cohomology of associative algebra bundles", Journal of the Ramanujan Mathematical Society, 9 (1): 1–12
Hecke algebra of a locally compact group (405 words) [view diff] exact match in snippet view article find links to article
of compact support C[K\G/K] can be endowed with a structure of an associative algebra under the operation of convolution. This algebra is denoted H(G//K)
Iwahori–Hecke algebra (2,025 words) [view diff] exact match in snippet view article find links to article
characteristic zero, then the one parameter Hecke algebra is a semisimple associative algebra over R[q±1]. Moreover, extending earlier results of Benson and Curtis
(2,3,7) triangle group (775 words) [view diff] exact match in snippet view article
group of norm 1 elements in the quaternion algebra generated as an associative algebra by the pair of generators i,j and relations i2 = j2 = η, ij = −ji
Standard complex (338 words) [view diff] exact match in snippet view article find links to article
⊗{\displaystyle \otimes } in their notation for the complex. If A is an associative algebra over a field K, the standard complex is ⋯→A⊗A⊗A→A⊗A→A→0,{\displaystyle
Partially ordered set (5,366 words) [view diff] exact match in snippet view article find links to article
displaying wikidata descriptions as a fallback Incidence algebra – associative algebra used in combinatorics, a branch of mathematicsPages displaying wikidata
Kasch ring (738 words) [view diff] exact match in snippet view article find links to article
Carl (1999), Rings and things and a fine array of twentieth century associative algebra, Mathematical Surveys and Monographs, vol. 65, Providence, RI: American
Linear algebra (7,687 words) [view diff] case mismatch in snippet view article find links to article
the theory of determinants". Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later
Bracket (mathematics) (1,789 words) [view diff] exact match in snippet view article
{\mathfrak {g}}}. By using the commutator as a Lie bracket, every associative algebra can be turned into a Lie algebra. There are many different forms
Charles Jasper Joly (477 words) [view diff] exact match in snippet view article find links to article
joining corresponding points. Proceedings RIA 4(4): 515. 1898: The associative algebra applicable to hyperspace. Proceedings R.I.A. 5(1):73 to 123. 1899:
Free Lie algebra (1,267 words) [view diff] exact match in snippet view article find links to article
enveloping algebra of a free Lie algebra on a set X is the free associative algebra generated by X. By the Poincaré–Birkhoff–Witt theorem it is the "same
Bicomplex number (1,711 words) [view diff] exact match in snippet view article find links to article
Commutative, associative algebra of two complex dimensions
Olive Hazlett (863 words) [view diff] case mismatch in snippet view article find links to article
1924, the same year she gave a talk on The Arithmetic of a General Associative Algebra at the International Congress of Mathematicians in Toronto, but in
Joseph A. Thas (451 words) [view diff] exact match in snippet view article find links to article
ratio of an ordered point quadruple on the projective line over an associative algebra with a unity element", Simon Stevin 42: 97−111 MR0266032 Thas, Joseph
Bolza surface (1,811 words) [view diff] exact match in snippet view article find links to article
over Q(2){\displaystyle \mathbb {Q} ({\sqrt {2}})} generated as an associative algebra by generators i,j and relations i2=−3,j2=2,ij=−ji,{\displaystyle
Birman–Wenzl algebra (1,167 words) [view diff] exact match in snippet view article find links to article
also be interpreted as a function F{\displaystyle F} on a certain associative algebra. In 1989, Birman & Wenzl (1989) constructed a two-parameter family
Dual number (2,605 words) [view diff] exact match in snippet view article find links to article
they are (trivially) zero divisors and clearly form an ideal of the associative algebra (and thus ring) of the dual numbers. The dual number a+bϵ{\displaystyle
Balanced module (791 words) [view diff] exact match in snippet view article find links to article
Carl (1999), Rings and things and a fine array of twentieth century associative algebra, Mathematical Surveys and Monographs, vol. 65, Providence, RI: American
Poincaré–Birkhoff–Witt theorem (1,885 words) [view diff] exact match in snippet view article find links to article
Lie algebra over a field is isomorphic to a Lie subalgebra of an associative algebra. Already at its earliest stages, it was known that K could be replaced
Gerhard Hochschild (687 words) [view diff] exact match in snippet view article find links to article
Hochschild–Mostow group Hochschild, G. (1945), "On the cohomology groups of an associative algebra", Annals of Mathematics, Second Series, 46 (1): 58–67, doi:10.2307/1969145
Algebra extension (821 words) [view diff] exact match in snippet view article find links to article
ISBN 978-3-540-30615-3. algebra extension at nLab infinitesimal extension at nLab Extension of an associative algebra at Encyclopedia of Mathematics
Irreducible representation (2,707 words) [view diff] exact match in snippet view article find links to article
equations. Simple module Indecomposable module Representation of an associative algebra Representation theory of Lie algebras Representation theory of SU(2)
Differential operator (3,409 words) [view diff] exact match in snippet view article find links to article
bidifferential operator. The notion appears, for instance, in an associative algebra structure on a deformation quantization of a Poisson algebra. A microdifferential
Scott W. Williams (1,328 words) [view diff] case mismatch in snippet view article find links to article
problems in The Mathematical Monthly and co-authored two papers on Non-Associative Algebra with his undergraduate advisor Dr. Volodymir Bohun-Chudyniv. Scott
Weak Hopf algebra (1,232 words) [view diff] exact match in snippet view article find links to article
H{\displaystyle H} such that (H,μ,η){\displaystyle (H,\mu ,\eta )} forms an associative algebra with multiplication μ:H⊗H→H{\displaystyle \mu :H\otimes H\rightarrow
Symmetric cone (16,254 words) [view diff] exact match in snippet view article find links to article
generate consists of all linear combinations of the ei. It is an associative algebra. If e is an idempotent, then 1 − e is an orthogonal idempotent. An
Philosophy of mathematics (10,289 words) [view diff] case mismatch in snippet view article find links to article
Peirce, Benjamin (1870), "Linear Associative Algebra", § 1. See Peirce, B. (1881). "Linear Associative Algebra". American Journal of Mathematics. 4
Diagonalizable matrix (3,675 words) [view diff] exact match in snippet view article find links to article
operator Diagonalizable group Jordan normal form Weight module – associative algebra generalization Orthogonal diagonalization Horn, Roger A.; Johnson
Adolph Winkler Goodman (893 words) [view diff] case mismatch in snippet view article find links to article
Places". Rings And Things And A Fine Array Of Twentieth Century Associative Algebra. Mathematical Surveys and Monographs. American Mathematical Society
Octonion (4,251 words) [view diff] exact match in snippet view article find links to article
2 Octonion algebra and its regular bimodule representation", Non-associative algebra and its applications, CRC Press, p. 235, ISBN 0-8247-2669-3 Rafał
Distribution on a linear algebraic group (1,100 words) [view diff] exact match in snippet view article find links to article
\Delta =\Delta \otimes 1\circ \Delta } ) and thus Dist(G) is an associative algebra, as the set is closed under the muplication by the formula: (*) Δ
List of Armenian inventors and discoverers (3,604 words) [view diff] case mismatch in snippet view article find links to article
Carl (2004). Rings And Things And A Fine Array Of Twentieth Century Associative Algebra (Mathematical Surveys and Monographs Volume 65). American Mathematical
Serial module (2,248 words) [view diff] exact match in snippet view article find links to article
Carl (1999), Rings and things and a fine array of twentieth century associative algebra, Mathematical Surveys and Monographs, 65. American Mathematical Society
Klein quartic (3,255 words) [view diff] exact match in snippet view article find links to article
elements of unit norm in the quaternion algebra generated as an associative algebra by the generators i,j and relations i2=j2=η,ij=−ji.{\displaystyle
Seven-dimensional cross product (4,442 words) [view diff] exact match in snippet view article find links to article
2 Octonion algebra and its regular bimodule representation". Non-associative algebra and its applications. CRC Press. p. 235. ISBN 0-8247-2669-3. Rafał
Charles Sanders Peirce bibliography (21,965 words) [view diff] case mismatch in snippet view article find links to article
Benjamin, "Linear Associative Algebra", American Journal of Mathematics v. 4, pp. 221-226, republished 1882 as Linear Associative Algebra with the addenda
Mathematics (16,256 words) [view diff] exact match in snippet view article find links to article
Peirce, Benjamin (1881). Peirce, Charles Sanders (ed.). "Linear associative algebra". American Journal of Mathematics. 4 (1–4) (Corrected, expanded,
Two-dimensional conformal field theory (5,090 words) [view diff] exact match in snippet view article find links to article
CFTs, the symmetry algebra is not just the Virasoro algebra, but an associative algebra (i.e. not necessarily a Lie algebra) that contains the Virasoro algebra
Projective line over a ring (2,856 words) [view diff] exact match in snippet view article find links to article
ratio of an ordered point quadruple on the projective line over an associative algebra with at unity element" (in Dutch) Simon Stevin 42:97–111 MR0266032
Method of quantum characteristics (3,752 words) [view diff] exact match in snippet view article find links to article
vector space V{\displaystyle \mathbb {V} } is endowed thereby with an associative algebra structure. Given two functions f(ξ)=Tr[B^(ξ)f^]  and  g(ξ)=Tr[B^(ξ)g^]
Differential algebra (7,430 words) [view diff] exact match in snippet view article find links to article
{g}})} of Lie algebra g{\textstyle {\mathcal {g}}} is a maximal associative algebra with identity, generated by Lie algebra elements g{\textstyle {\mathcal
List of women in mathematics (21,978 words) [view diff] exact match in snippet view article find links to article
doctorate Anastasia Stavrova, Russian expert in algebraic groups, non-associative algebra, and algebraic K-theory Jackie Stedall (1950–2014), British historian
Mutation (Jordan algebra) (15,829 words) [view diff] exact match in snippet view article
f2 are orthogonal. In this case e1 and e2 generate a commutative associative algebra and e1e2 = 0, since (e1e2,e1e2) =(f1,f2) =0. Let a be in Eτ. Let