Liftings of graded quasi-Hopf algebras with radical of prime codimension
Liftings of graded quasi-Hopf algebras with radical of prime codimension
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DOI：
10.1016/j.jpaa.2005.06.016
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发表时间：
2004-12
影响因子：
0.8
通讯作者：
P. Etingof;Shlomo Gelaki
中科院分区：
文献类型：
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作者：
P. Etingof;Shlomo Gelaki
设p为素数，设RG(p)表示C上的根具有余维数p的根本渐变有限维拟hopf代数的等价类集合。本文的目的是对根为拟hopf理想且余维数p的有限维拟hopf代数a进行分类；即A在RG(p)中具有gr(A)，其中gr(A)是对A上的根过滤取的相关的分级代数。本文的主要结果是以下定理：设A是一个有限维的拟Hopf代数，其根是素数余维p的拟Hopf理想。那么A要么是扭曲等价于Hopf代数，要么是扭曲等价于H(2)、H±(p)、A(q)、H(32)，构造于。注意，任何简单对象可逆且在张量下形成p阶群的有限张量范畴都是上述拟hopf代数a的表示范畴。因此，本文对这些类别进行了分类。
Let p be a prime, and let RG(p) denote the set of equivalence classes of radically graded finite dimensional quasi-Hopf algebras over C, whose radical has codimension p. The purpose of this paper is to classify finite dimensional quasi-Hopf algebras A whose radical is a quasi-Hopf ideal and has codimension p; that is, A with gr(A) in RG(p), where gr(A) is the associated graded algebra taken with respect to the radical filtration on A. The main result of this paper is the following theorem: Let A be a finite dimensional quasi-Hopf algebra whose radical is a quasi-Hopf ideal of prime codimension p. Then either A is twist equivalent to a Hopf algebra, or it is twist equivalent to H(2), H±(p), A(q), or H(32), constructed in . Note that any finite tensor category whose simple objects are invertible and form a group of order p under tensor is the representation category of a quasi-Hopf algebra A as above. Thus this paper provides a classification of such categories.