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Diagrams of Hopf algebras with the Chevalley property

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Abstract

In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf subalgebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A’s diagram equaling the diagram of its maximal pointed Hopf subalgebra.

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Authors and Affiliations

  1. School of Mathematical Science, Ocean University of China, Qingdao, 266100, China

    Zhong-ping Fan

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Di-ming Lu

  3. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, China

    Xiao-lan Yu

Authors
  1. Zhong-ping Fan
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  2. Di-ming Lu
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  3. Xiao-lan Yu
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Corresponding author

Correspondence to Zhong-ping Fan.

Additional information

Supported by the National Natural Science Foundation of China (11271319, 11301126).

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Fan, Zp., Lu, Dm. & Yu, Xl. Diagrams of Hopf algebras with the Chevalley property. Appl. Math. J. Chin. Univ. 31, 367–378 (2016). https://doi.org/10.1007/s11766-016-3403-2

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  • DOI: https://doi.org/10.1007/s11766-016-3403-2

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