2024 Triangular hopf algebra

Triangular hopf algebra

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August undefined, 2024

http://homepages.math.uic.edu/~kauffman/Hopf.pdf WebWe say that a Hopf algebra has the Chevalley property if the tensor product of any two simple modules over this Hopf algebra is semisimple. In this paper we classify finite dimensional triangular Hopf algebras with the Chevalley property, over the field of …

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WebWe say that a Hopf algebra has the Chevalley property if the tensor product of any two simple modules over this Hopf algebra is semisimple. In this paper we classify finite … WebDec 1, 2024 · Let (H, R) be a quasi-triangular Hopf algebra, then there is a 1-1 correspondence between the set of the non-isomorphic 1-dimensional Yetter-Drinfeld modules in YD H H and the set Z G (H) × {the non-isomorphic 1-dimensional left modules of H}. Proof. Let V = k v be a 1-dimensional Yetter-Drinfeld module in YD H H. glan ifron

Quasi-triangular quasi-Hopf algebra - Wikipedia

WebThe paper is organized as follows. Section 1 recalls Hopf algebras, quasi-triangular Hopf algebras and ribbon Hopf algebras. Section 2 discusses the conceptual setting of the … WebJul 16, 1999 · A fundamental problem in the theory of Hopf algebras is the classification and construction of finite-dimensional (minimal) triangular Hopf algebras (A,R) introduced by … WebNov 3, 2001 · By [1], [15] the triangular Hopf algebra A, with R-matrix R g is the key model of finite-dimensional triangular Hopf algebras over C. Indeed, all other such Hopf algebras are obtained from a Hopf ... glan irfon hospital

Quasitriangular Hopf algebra - Wikipedia

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WebIt was recently discovered ([AEG], [EG1]) that the twisting procedure of finite supergroups can be used to construct new families of triangular Hopf algebras. Furthermore, it turned out that these families exhaust all triangular Hopf algebras with the Chevalley property (in particular, all previously known triangular Hopf algebras). WebNov 14, 2024 · Download a PDF of the paper titled On the Structure of Irreducible Yetter-Drinfeld Modules over Quasi-Triangular Hopf Algebras, by Zhimin Liu and 1 other authors glanis healthcareWebJan 24, 2024 · Lie brackets on Hopf algebra cohomology. Tekin Karadağ, Sarah Witherspoon. By work of Farinati, Solberg, and Taillefer, it is known that the Hopf algebra cohomology of a quasi-triangular Hopf algebra, as a graded Lie algebra under the Gerstenhaber bracket, is abelian. Motivated by the question of whether this holds for … fws nctc

"WebIt was recently discovered ([AEG], [EG1]) that the twisting procedure of finite supergroups can be used to construct new families of triangular Hopf algebras. Furthermore, it turned … " - Triangular hopf algebra

Triangular hopf algebra

WebSep 14, 2016 · We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. … WebJul 1, 2024 · We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of the Taft algebra T p for any integer p > 2 which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of T p, as in all known quasi-triangular Hopf algebras.This example is the first known bracket …

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WebJan 30, 2024 · A braided symmetric algebra carries a representation of a triangular Hopf algebra. Its noncommutativity is captured by the universal R-matrix. Its differential geometry is canonically constructed from these data. We … WebThe Hopf algebra H(G;G +,G−) has been studied in [BGM] under a diﬀerent context.Despite what the title and the abstract may suggest, only the standard quasi-triangular structure …

WebAbstract: In this paper, we classify triangular semisimple and cosemisimple Hopf algebras over any algebraically closed field k. Namely, we construct, for each positive integer N, … WebMay 5, 2024 · A quasi-triangular Hopf algebra, introduced by Drinfel’d [56], consists of a Hopf algebra together with a special element \(\mathsf {R}\) called a universal R-matrix. The raison d’être of quasi-triangular Hopf algebra is, as suggested by the term “universal R-matrix”, that they give rise to solutions of the Yang–Baxter equation.

WebJan 30, 2024 · We calculate the Gerstenhaber bracket (graded Lie bracket) on Hopf algebra and Hochschild cohomologies of the Taft algebra \(T_n\) for any integer \(n> 2\) which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of \(T_n\), as in all known quasi-triangular Hopf algebras.This example is the … Webalgebra, coalgebra, bialgebra, Hopf algebra, triangular Hopf algebra, etc, to be an object of this category equipped with the usual structure maps (morphisms in this category), …

WebSep 30, 2000 · triangular Hopf algebra a twis t o f a mo diﬁed sup ergroup algebra? In the app endix w e use the Lifting metho d [AS1,AS2] to giv e other pro ofs of Theorem. 5.2.1 and Corollary 6.3, a nd a g ...

WebA Hopf algebra together with an universal R-matrix is called a quasitriangular Hopf algebra. The braiding V W= W V is then given by ˝R, where ˝is transposition. Among the class of quasitriangular Hopf algebras there are two extrema. Triangular Hopf algebras are those for which R 21R= 1 2A A. These give rise to symmetric braided categories. fws night differentialWebAug 20, 2024 · Let R: V ⊗ V → V ⊗ V be an endomorphism of V ⊗ V satisfying the Yang-Baxter equation. Then the reflection equation algebra if the algebra generated by elements ( a i j) 1 ≤ i, j ≤ n with relation. R A 1 R A 1 = A 1 R A 1 R. where A is the matrix n × n having the generating elements as coefficients and A 1 = A ⊗ I d . fws nlebWebJan 6, 2001 · Download PDF Abstract: Recall that a triangular Hopf algebra A is said to have the Chevalley property if the tensor product of any two simple A-modules is semisimple, or, equivalently, if the radical of A is a Hopf ideal. There are two reasons to study this class of triangular Hopf algebras: First, it contains all known examples of finite-dimensional … fws national wetlands inventoryWebA quasi-triangular quasi-Hopf algebra is a set where is a quasi-Hopf algebra and known as the R-matrix, is an invertible element such that. for all , where is the switch map given by , … fws nctc trainingWebJan 6, 2001 · Download PDF Abstract: Recall that a triangular Hopf algebra A is said to have the Chevalley property if the tensor product of any two simple A-modules is semisimple, … glan irfon builthWebSep 14, 2016 · We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. These module homomorphisms played a key role in his proof of a conjecture of Yau (1998). They will also be useful in the problem of decomposition of tensor products of modules. … fws new england field officeWebSep 14, 2008 · A sequence to compute the Brauer group of certain quasi-triangular Hopf algebras. A deeper understanding of recent computations of the Brauer group of Hopf algebras is attained by explaining why a direct product decomposition for this group holds and describing the non-interpreted factor occurring in it. For a Hopf algebra in a braided … glan irfon health centre