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arXiv · 1509.05837

Block Systems of finite dimensional non-cosemisimple Hopf Algebras

Z. -P. Fan·D. -M. Lu
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Abstract

In this paper, we study finite dimensional non-cosemisimple Hopf algebras through its underlying coalgebra. We decompose such a Hopf algebra as a direct sum of `blocks'. Blocks are closely related to each other by `rules' and form the `block system'. Through the block system, we are able to give a lower bound for $\dim H$, where $H$ is a non-cosemisimple Hopf algebras with no nontrivial skew-primitives, and a series of results about non-cosemisimple Hopf algebras of dimension $12p, 15p, 16p, 20p\ \text{and}\ 21p$ with $p$ being a prime number.

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BibTeXRIS

Z. -P. Fan, D. -M. Lu. 2015-09-19. Block Systems of finite dimensional non-cosemisimple Hopf Algebras. https://arxiv.org/abs/1509.05837

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