Classifying bicrossed products of two Taft algebras |
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Authors: | A.L. Agore |
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Affiliation: | 1. Faculty of Engineering, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium;2. “Simion Stoilow” Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania |
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Abstract: | We classify all Hopf algebras which factor through two Taft algebras and respectively . To start with, all possible matched pairs between the two Taft algebras are described: if then the matched pairs are in bijection with the group of d-th roots of unity in k, where while if then besides the matched pairs above we obtain an additional family of matched pairs indexed by . The corresponding bicrossed products (double cross product in Majid's terminology) are explicitly described by generators and relations and classified. As a consequence of our approach, we are able to compute the number of isomorphism types of these bicrossed products as well as to describe their automorphism groups. |
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Keywords: | 16T10 16T05 16S40 |
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