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• W2952109747 abstract "In this paper we continue the study started recently in cite{ABMbp} by describing and classifying all Hopf algebras $E$ that factorize through two Sweedler's Hopf algebras. Equivalently, we classify all bicrossed products $H_4 bowtie H_4$. There are three steps in our approach. First, we explicitly describe the set of all matched pairs $(H_4, H_4, triangleright, triangleleft)$ by proving that, with the exception of the trivial pair, this set is parameterized by the ground field $k$. Then, for any $lambda in k$, we describe by generators and relations the associated bicrossed product, mathcal{H}_{16, , lambda}$. This is a 16-dimensional, pointed, unimodular and non-semisimple Hopf algebra. A Hopf algebra $E$ factorizes through $H_4$ and $H_4$ if and only if $ E cong H_4 ot H_4$ or $E cong mathcal{H}_{16,, lambda}$. In the last step we classify these quantum groups by proving that there are only three isomorphism classes represented by: $H_4 ot H_4$, $mathcal{H}_{16, , 0}$ and $mathcal{H}_{16, , 1} cong D(H_4)$, the Drinfel'd double of $H_4$. The automorphism group of these objects is also computed: in particular, we prove that $Aut_{rm Hopf}big(D(H_4)big)$ is isomorphic to a semidirect product of groups, $k^{times} rtimes mathbb{Z}_2$." @default.
• W2952109747 created "2019-06-27" @default.
• W2952109747 creator A5084041749 @default.
• W2952109747 date "2012-05-31" @default.
• W2952109747 modified "2023-09-27" @default.
• W2952109747 title "Classifying bicrossed products of two Sweedler's Hopf algebras" @default.
• W2952109747 cites W1500084468 @default.
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• W2952109747 hasPublicationYear "2012" @default.
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