Constructing New Braided T-Categories over Weak Hopf Algebras
Constructing New Braided T-Categories over Weak Hopf Algebras
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DOI：
10.1007/s10485-008-9175-y
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发表时间：
2010-08
影响因子：
0.6
通讯作者：
Ling Liu;Shuanhong Wang
中科院分区：
文献类型：
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作者：
Ling Liu;Shuanhong Wang
设AutweakHopf（H）表示在Böhm等人（J Algebra 221：385-438，1999）意义下具有双射对极的弱Hopf代数H的所有自同构的集合，设G是某个交叉积群AutweakHopf（H）×AutweakHopf（H）.本文的主要目的是提供Turaev（1994，2008）意义下的辫子T-范畴的进一步例子。为此，我们首先引入了一类新的弱（α，β）-Yetter-Drinfeld模范畴，其中α，β∈AutweakHopf（H），并证明了这类范畴成为G上的辫子T-范畴，推广了Panaite和Staic（Isr J Math 158：349-365，2007）的主要构造.最后，当H是有限维时，我们在弱Smash积代数族上构造了一个拟三角弱T-余代数WD（H）= {WD（H）（α，β）}（α，β）∈ G（在货车Daele和Wang（Comm Algebra，2008）意义下），并得到了它同构于拟三角弱T-余代数WD（H）的表示范畴.
LetAutweakHopf(H) denote the set of all automorphisms of a weak Hopf algebraHwith bijective antipode in the sense of Böhm et al. (J Algebra 221:385–438, 1999) and letGbe a certain crossed product groupAutweakHopf(H)×AutweakHopf(H). The main purpose of this paper is to provide further examples of braidedT-categories in the sense of Turaev (1994, 2008). For this, we first introduce a class of new categoriesof weak (α,β)-Yetter-Drinfeld modules withα,β∈AutweakHopf(H) and we show that the categorybecomes a braidedT-category overG, generalizing the main constructions by Panaite and Staic (Isr J Math 158:349–365, 2007). Finally, whenHis finite-dimensional we construct a quasitriangular weakT-coalgebraWD(H) = {WD(H)(α,β)}(α,β) ∈Gin the sense of Van Daele and Wang (Comm Algebra, 2008) over a family of weak smash product algebras, and we obtain thatis isomorphic to the representation category of the quasitriangular weakT-coalgebraWD(H).