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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 72 found (296 total)

alternate case: associative algebra

Supercommutative algebra (310 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 (1,186 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 (2,107 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 + b i + c

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 (805 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

Latin square (3,698 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

Moufang loop (1,738 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

Isotopy of loops (838 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

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

Heap (mathematics) (1,470 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

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

Lie conformal algebra (447 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

Biracks and biquandles (1,025 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 (4,077 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 (864 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 (283 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 (2,887 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

Octonion algebra (818 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

Nilpotent (1,183 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

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 (8,900 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 (3,281 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 (3,394 words) [view diff] exact match in snippet view article find links to article

and the homology ring H H ∗ ( A ) {\displaystyle HH_{*}(A)} for an associative algebra A {\displaystyle A} . For the case of commutative algebras, there

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 (2,051 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 (818 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 (347 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

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

Partially ordered set (5,544 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

Linear algebra (7,778 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) (1,821 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:

Bicomplex number (1,767 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 (453 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

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 (1,922 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

Dual number (2,754 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 + b ϵ {\displaystyle

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 (837 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

Birman–Wenzl algebra (1,364 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

Irreducible representation (2,787 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 (3,650 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

Symmetric cone (16,607 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

Weak Hopf algebra (1,312 words) [view diff] exact match in snippet view article find links to article

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

Philosophy of mathematics (10,342 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

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

Diagonalizable matrix (4,044 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

Octonion (4,419 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 (2,268 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 (3,288 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 i 2 = j 2 = η , i j = − j i

Seven-dimensional cross product (4,403 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 (16,258 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 (5,439 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 (2,906 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 (3,908 words) [view diff] exact match in snippet view article find links to article

space V {\displaystyle \mathbb {V} } is endowed thereby with an associative algebra structure. Given two functions f ( ξ ) = T r [ B ^ ( ξ ) f ^ ]

Differential algebra (7,867 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 (22,165 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) (15,817 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