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- {{Short description|Non-associative algebras with positive-definite quadratic form}} ...Such algebras, sometimes called '''Hurwitz algebras''', are examples of [[composition algebra]]s. ...28 KB (4,092 words) - 18:15, 8 February 2025
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- ...ariety of [[group (mathematics)|groups]], consist of congruence-permutable algebras, but some, like the variety of [[lattice (order)|lattices]], have members t ...> permute.{{r|Bergman|p=122}} A [[variety (universal algebra)|variety]] of algebras <math>\mathcal{V}</math> is referred to as '''congruence-permutable''' when ...3 KB (405 words) - 15:23, 17 December 2020
- ...{{harvs|txt|first=Susumu|last=Okubo|year=1978}}</ref> Okubo algebras are [[composition algebra]]s, [[flexible algebra]]s (''A''(''BA'') = (''AB'')''A'') ..., [[Alexander Merkurjev]], [[Markus Rost]], [[Jean-Pierre Tignol]] (1998) "Composition and Triality", chapter 8 in ''The Book of Involutions'', pp 451–511, Colloq ...7 KB (930 words) - 16:50, 21 February 2024
- ...the '''Lie operad''' is an [[operad theory|operad]] [[Operad algebra|whose algebras]] are [[Lie algebra]]s. The notion (at least one version) was introduced by ...nder that action, <math>\mathcal{Lie}(n)</math> is invariant. The operadic composition is given by substituting expressions (with renumbered variables) for variab ...2 KB (261 words) - 04:15, 13 May 2024
- ...of '''C''') that satisfies the following conditions:<ref name="dimensional-algebras">{{harvnb|Cline|Parshall|Scott|1988|loc=§3}}</ref> ...e, a composition factor of an object ''A'' in '''C''' is, by definition, a composition factor of one of its finite length subobjects.</ref> ...4 KB (550 words) - 02:16, 25 April 2023
- ...ike [[Permutation|permutations]] ([[Bijection|bijective mappings]]). These algebras provide intriguing connections between mathematical concepts and are classi ...ial">{{cite journal |last1=Pálfy |first1=P. P. |title=Unary polynomials in algebras. I |journal=Algebra Universalis |date=1984 |volume=18 |issue=3 |pages=262–2 ...3 KB (407 words) - 10:20, 23 August 2024
- ...>f</math> onto <math>S</math> can be defined as the [[function composition|composition]] <math>f|_S = f\circ i_S</math>. ...a [[quotient space (topology)|quotient map]]) then Andreotti considers the composition <math>p^U\circ f:A\to U</math>, which surely always exists. ...3 KB (455 words) - 14:40, 19 September 2024
- ...)</math>, with composition given by the usual bilinear rule, extending the composition of <math>\mathsf{G}</math>.<ref>{{harvnb|Mosa|1986}}</ref> [[Category:Algebras]] ...4 KB (586 words) - 15:41, 21 February 2022
- ...e ''Samelson subspace'', are those primitive elements in the kernel of the composition <math>P \overset\tau\to S(\mathfrak{g}^*) \to S(\mathfrak{k}^*)</math>, [[Category:Lie algebras]] ...3 KB (452 words) - 18:59, 13 July 2021
- ...groups]] like <math>SU_q(3)</math> can be realised as the <math>C^*</math>-algebras of <math>k</math>-graphs.<ref>{{citation |first1=O.|last1=Giselsson |title= ...t1=A.|last1=Sims |title=''Lecture notes on higher-rank graphs and their C*-algebras''|url=https://www.aidansims.com/files/k-graphNotes2010.pdf}}</ref> In parti ...8 KB (1,322 words) - 14:00, 9 October 2024
- ...a quadratic form admitting composition, and hence the bioctonions form a [[composition algebra]]. [[Category:Composition algebras]] ...3 KB (468 words) - 16:31, 27 July 2023
- ..., 316–320. {{doi|10.1006/jabr.1996.0067}} {{MR|1375581}}</ref> Schur algebras were used by Friedlander and [[Andrei Suslin|Suslin]] to [[mathematical pro * Schur algebras are "defined over the integers". This means that they satisfy the following ...9 KB (1,309 words) - 18:11, 14 August 2024
- ...nd scalars on [[group ring|group algebra]]s and also on modules over group algebras, i.e., [[group representation]]s. Particularly useful is relating how [[irr ...math>, define <math>Fu : M^S \to N</math> to be the [[function composition|composition]] ...9 KB (1,496 words) - 02:33, 9 January 2025
- ...milar functors '''Exal''' and '''Exan''' for [[non-commutative ring]]s and algebras, and functors '''Exaltop''', '''Exantop''', and '''Exalcotop''' that take a ...ns must be defined. Fix a [[topos]] <math>T</math> and let all algebras be algebras over it. Note that the topos of a point gives the special case of commutati ...11 KB (1,780 words) - 00:50, 28 October 2024
- === Ext Algebras === ...mations | last=Illusie | first=Luc | page=163}}</ref> For example, given a composition of ringed topoi <math display="block">X \xrightarrow{f} Y \to S</math> and ...4 KB (670 words) - 21:33, 19 June 2023
- ...], is a certain type of '''[[AT algebra]]''', a [[direct limit]] of matrix algebras over the continuous functions on the circle, in which the connecting maps a ...her with the fact that they are AT, this implies they have [[real rank (C*-algebras)#Real rank zero|real rank zero]]. ...14 KB (1,887 words) - 08:04, 25 January 2024
- ...which fixes the [[origin (mathematics)|origin]]. It can be written as the composition of an [[orthogonal transformation]] (an origin-preserving [[rigid transform ...)|reflection]] or dilation is a conformal linear transformation, as is any composition of these basic transformations, including [[rotation]]s and [[improper rota ...6 KB (893 words) - 05:44, 9 February 2024
- ...bras over a noncommutative base ring, where weak Hopf algebras become Hopf algebras over a [[separable algebra]]. It is a theorem that a Hopf algebroid satisf ...der the category <math>\text{CRing}_k</math> of commutative <math>k</math>-algebras. ...14 KB (2,138 words) - 16:24, 28 September 2024
- ...Curtis |year=1963 |section=The four and eight square problem and division algebras |title=Studies in Modern Algebra |editor=Albert, A.A. |pages=100–125, esp. * [[Composition algebra]] ...4 KB (561 words) - 19:50, 10 October 2024
- The [[coproducts]] are classical, and encode the group composition law: [[Category:Hopf algebras]] ...3 KB (391 words) - 15:00, 9 January 2025
- ...>''p''</sub> extensions in [[Iwasawa theory]], and non-commutative Iwasawa algebras of compact [[Pro-p group|''p''-adic analytic groups]] were introduced by {{ ...owiki>/(''f'') occurs in the module is well defined and independent of the composition series. The torsion module therefore has a '''characteristic power series'' ...9 KB (1,285 words) - 09:57, 7 November 2023