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CLC number: O153.3
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Received: 2005-10-08
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Almost split sequences for symmetric non-semisimple Hopf algebras
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SHI Mei-hua. Almost split sequences for symmetric non-semisimple Hopf algebras[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1077-1083.
@article{title="Almost split sequences for symmetric non-semisimple Hopf algebras",
author="SHI Mei-hua",
journal="Journal of Zhejiang University Science A",
volume="7",
number="6",
pages="1077-1083",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1077"
}
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%DOI 10.1631/jzus.2006.A1077
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T1 - Almost split sequences for symmetric non-semisimple Hopf algebras
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J0 - Journal of Zhejiang University Science A
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SP - 1077
EP - 1083
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A1077
Abstract: We first prove that for a finite dimensional non-semisimple Hopf algebra H, the trivial H-module is not projective and so the almost split sequence ended with k exists. By this exact sequence, for all indecomposable H-module X, we can construct a special kind of exact sequence ending with it. The main aim of this paper is to determine when this special exact sequence is an almost split one. For this aim, we restrict H to be unimodular and the square of its antipode to be an inner automorphism. As a special case, we give an application to the quantum double D(H)=(Hop)*⋈H) of any non-semisimple Hopf algebra.
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