Crossed modules of associative algebras
WebarXiv:math/0311316v2 [math.QA] 23 Feb 2004 Quantum groupoids and dynamical categories∗ J. Donin† and A. Mudrov‡ †,‡Department of Mathematics, Bar Ilan University, 52900 WebYang-Baxter equation, Yetter-Drinfel′d module, Hopf algebra, self-distributivity, crossed module of groups, crossed module of racks, crossed module of Lie algebras, braided system, monoidal category, associator. 1 2 VICTORIA LEBED AND FRIEDRICH WAGEMANN FIGURE1.
Crossed modules of associative algebras
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WebJan 1, 2016 · We will consider in total five categories of crossed modules, namely: crossed modules of Lie algebras and of (Lie) groups (already mentioned), and, in addition, … WebOct 25, 2024 · This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written …
Webadditive K-theory of associative algebras. The theory of Lie superalgebras, also called Z 2-graded Lie algebras, has aroused much interest both in mathematics and physics. Lie superalgebras play a very ... efficients in crossed modules. We show that, if the crossed module is a supermodule, then the non-abelian homology is the usual homology of ... WebAdjoint functors between the categories of crossed modules in dialgebras and Leibniz algebras are constructed. The well known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the respective categories of crossed modules. Communicated by I. Shestakov Keywords: Leibniz algebra associative dialgebra
WebExamples of associative algebras include the algebra of all n -by- n matrices over a field (or commutative ring) K. Here the multiplication is ordinary matrix multiplication. group algebras, where a group serves as a basis of the vector space and algebra multiplication extends group multiplication. WebOct 29, 2024 · Idea 0.1. The notion of Lie–Rinehart pair is an algebraic encoding of the notion of Lie algebroid. It is the pair consisting of the associative algebra of functions on the base space of the Lie algebroid and of the Lie algebra of its global sections. The anchor map of the Lie algebroid is encoded in the action of the Lie algebra on the ...
WebApr 23, 2024 · A crossed module of associative R - algebras is a morphism \mu :\mathrm {M} \rightarrow \mathrm {A} of associative R -algebras where \mathrm {A} is unitary and has an associative action on \mathrm {M} and where the same axioms as CM1 and CM2 of Definition 2.6 are satisfied for all a,a^ {\prime }\in \mathrm {A} and m,m^ {\prime }\in …
WebDec 12, 1995 · The notion of crossed modules for Lie 2-algebras is defined and a strict Lie 3-algebra structure is associated to a given crossed module and its mapping cone complex and its derivations are associated. 8 PDF View 1 excerpt, cites background ℤ2-GRADED POISSON ALGEBRAS, THEIR DEFORMATIONS AND COHOMOLOGY IN LOW … nixon ins agcy \\u0026 brkg svcsWebJun 21, 2015 · Mathematics. arXiv: Rings and Algebras. The aim of this paper is to review the deformation theory of n-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and … nixon in china playWebIn this paper, we want to describe an analogous philosophy for crossed modules of associative algebras, which will be called crossed modules of algebras hereafter. The results are important for examining the rst cyclic homology of associative algebras, in terms of Hopf-type formulas. nixon house saddle riverWebMay 5, 2024 · Crossed modules, non-abelian extensions of associative conformal algebras and Wells exact sequences Preprint Full-text available Nov 2024 Bo Hou Jun Zhao View Show abstract ... Cohomology... nursing evaluation for risk of infectionWebcategories of Lie and associative algebras. The aim of this paper is to extend this adjunction to the categories of crossed modules of Leibniz algebras and dialgebras, and to establish … nursing evaluation for fall riskWebGiven an associative 2-algebra (A1;A0;s;t;i;–), the corresponding crossed module is (R;A;‰), whereR= Kers,A=A0,„=t jKers, and the action ofAonRis given bya ¢ r=i(a)† randr ¢ a=r † i(a), fora... nursing evaluation for feverWebJul 21, 2024 · Moreover, the reader will be introduced to a new type of algebras called noncommutative Leibniz–Poisson algebras, with their properties and cohomology theory and the relationship of new cohomologies with well-known cohomologies of underlying associative and Leibniz algebras. nursing evaluation for hypertension