Finite quasi-quantum groups of diagonal type
Abstract
The goal of the present paper is to classify an interesting class of elementary quasi-Hopf algebras, or equivalently, finite-dimensional pointed Majid algebras. By a Tannaka-Krein type duality, this determines a big class of pointed finite tensor categories. Based on some interesting observations of normalized 3-cocycles on finite abelian groups, we elucidate an explicit connection between our objective pointed Majid algebras and finite-dimensional pointed Hopf algebras over finite abelian groups. With a help of this connection and the successful theory of diagonal Nichols algebras over abelian groups, we provide a conceptual classification of finite-dimensional graded pointed Majid algebras of diagonal type. Some efficient methods of construction are also given.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.04096
- arXiv:
- arXiv:1611.04096
- Bibcode:
- 2016arXiv161104096H
- Keywords:
-
- Mathematics - Quantum Algebra;
- 16T05;
- 18D10;
- 16G60
- E-Print:
- 35pages. All comments are welcome