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arXiv · 1706.08446

Finite-dimensional quasi-Hopf algebras of Cartan type

Yuping Yang·Yinhuo Zhang
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Abstract

In this paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of finite-dimensional radically graded basic quasi-Hopf algebras over abelian groups with dimensions not divisible by $2,3,5,7$ and associators given by abelian $3$-cocycles. As special cases , the small quasi-quantum groups are introduced and studied. Many new explicit examples of finite-dimensional genuine quasi-Hopf algebras are obtained.

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Yuping Yang, Yinhuo Zhang. 2017-06-26. Finite-dimensional quasi-Hopf algebras of Cartan type. https://arxiv.org/abs/1706.08446

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