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- W2953085508 abstract "It is shown in math.QA/0310253 that a finite dimensional quasi-Hopf algebra over the complex numbers with radical of codimension 2 is twist equivalent to a Nichols Hopf algebra, or to a lifting of one of four special quasi-Hopf algebras of dimensions 2, 8, 8, and 32. The purpose of this paper is to construct new finite dimensional basic quasi-Hopf algebras A(q) of dimension n^3, n>2, parametrized by primitive roots of unity q of order n^2, with radical of codimension n, which generalize the construction of the basic quasi-Hopf algebras of dimension 8 given in math.QA/0310253. These quasi-Hopf algebras are not twist equivalent to a Hopf algebra, and may be regarded as quasi-Hopf analogs of Taft Hopf algebras. By math.QA/0301027, our construction is equivalent to the construction of new finite tensor categories whose simple objects form a cyclic group of order n, and which are not tensor equivalent to a representation category of a Hopf algebra. In a later publication we plan to use our construction to classify finite tensor categories whose simple objects form a cyclic group of prime order n. We also prove that if H is a finite dimensional radically graded quasi-Hopf algebra with H[0]=(C[Z/nZ],Phi), where n is prime and Phi is a nontrivial associator, such that H[1] is a free left module over H[0] of rank 1 (it is always free) then H is isomorphic to A(q)." @default.
- W2953085508 created "2019-06-27" @default.
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- W2953085508 date "2004-02-10" @default.
- W2953085508 modified "2023-09-27" @default.
- W2953085508 title "Basic quasi-Hopf algebras of dimension n^3" @default.
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