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Subjects
16-XX Associative rings and algebras
16Txx Hopf algebras, quantum groups and related topics
16T10 Bialgebras

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The bicrossed products of $H_{4}$ and $H_{8}$

Daowei Lu, Yan Ning, Dingguo Wang (2020)

Czechoslovak Mathematical Journal

Let $H_{4}$ and $H_{8}$ be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through $H_{8}$ and $H_{4}$ (equivalently, any bicrossed product between the Hopf algebras $H_{8}$ and $H_{4}$ ) must be isomorphic to one of the following four Hopf algebras: $H_{8} \otimes H_{4}, H_{32, 1}, H_{32, 2}, H_{32, 3}$ . The set of all matched pairs $(H_{8}, H_{4}, ▹, ◃)$ is explicitly described, and then the associated bicrossed product is given by generators and relations.

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