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Find link is a tool written by Edward Betts.Longer titles found: Non-associative algebra (view), Commutant-associative algebra (view), Free product of associative algebras (view), Homotopy associative algebra (view)
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Supercommutative algebra
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In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y weMoufang 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 rankJacobi identity (1,241 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, ∗) hasHyperbolic 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 + cMonster 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 LepowskyCH-quasigroup (59 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 abelianBol 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 mathematicianAdmissible algebra (64 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 sumIsotopy 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 andMoufang loop (1,788 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 loopsLatin square (3,757 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 rowHeap (mathematics) (1,471 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 {\displaystyleQuasifield (808 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 \cdotBiracks 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 knotsGyrovector space (4,090 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 978-0-8247-2669-0Medial magma (865 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 (3,515 words) [view diff] no match in snippet view article find links to article
Latin squares and finite quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraicJacobson–Bourbaki theorem (443 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 correspondenceIdempotence (2,941 words) [view diff] exact match in snippet view article find links to article
Sciences (Washington, DC, USA): Peirce, Benjamin (1870) "Linear associative algebra" From pages 16-17: "When an expression which is raised to the squareCyclotomic 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 functionCommutator 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. MembersOctonion algebra (820 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 normNilpotent (1,210 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 definitionQuadratic 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 definedVertex operator algebra (8,938 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 stringHall 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 basisHochschild homology (3,399 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, thereAlgebra 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): 1–12Joseph A. Thas (467 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(2,3,7) triangle group (830 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 = −jiCharles Jasper Joly (605 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:Partially ordered set (5,378 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 mathematics Lattice – Set whoseOlive Hazlett (864 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 inKasch ring (766 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: AmericanFree Lie algebra (1,272 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 "sameGerhard 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:10.2307/1969145Linear algebra (7,974 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 laterBicomplex number (1,806 words) [view diff] exact match in snippet view article find links to article
Commutative, associative algebra of two complex dimensionsHecke algebra of a pair (666 words) [view diff] exact match in snippet view article find links to article
compact support Cc∞[K\G/K] can be endowed with a structure of an associative algebra under the operation of convolution. This algebra is often denotedPoincaré–Birkhoff–Witt theorem (1,934 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 replacedBalanced 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: AmericanBracket (mathematics) (1,824 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 formsDual number (2,780 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 {\displaystyleAdolph Winkler Goodman (899 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 SocietyScott 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. Volodymyr Bohun-Chudinov. ScottIrreducible representation (2,824 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)Algebra extension (842 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 MathematicsBolza surface (2,077 words) [view diff] exact match in snippet view article find links to article
( 2 ) {\displaystyle \mathbb {Q} ({\sqrt {2}})} generated as an associative algebra by generators i,j and relations i 2 = − 3 , j 2 = 2 , i j = − j iDifferential operator (3,693 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 microdifferentialLie superalgebra (2,397 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathfrak {gl}}(p|q)} . A Poisson algebra is an associative algebra together with a Lie bracket. If the algebra is given a Z2-gradingSymmetric cone (16,613 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. AnWeak Hopf algebra (1,313 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\rightarrowDistribution 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: (*) ΔKlein quartic (3,263 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 iDiagonalizable matrix (4,692 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.; JohnsonOctonion (5,316 words) [view diff] case mismatch in snippet view article find links to article
2 Octonion algebra and its regular bimodule representation", Non-Associative Algebra and its Applications, Boca Raton, FL: CRC Press, p. 235, ISBN 0-8247-2669-3Serial module (2,263 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 SocietyList of Armenian inventors and discoverers (3,832 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 MathematicalSeven-dimensional cross product (4,787 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. RafałCharles Sanders Peirce bibliography (21,902 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 addendaMathematics (15,937 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 (5,674 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 algebraProjective line over a ring (2,979 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 MR0266032Method 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 (7,852 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 {\mathcalList of women in mathematics (23,282 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 historianMutation (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