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The planar algebra of a semisimple and cosemisimple Hopf algebra

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Abstract

To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with non-zero modulus and of depth two. This association is shown to yield a bijection between (the isomorphism classes, on both sides, of) such objects.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, 600 113, Taramani, Chennai, India

    Vijay Kodiyalam & V. S. Sunder

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  1. Vijay Kodiyalam
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  2. V. S. Sunder
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Correspondence to Vijay Kodiyalam.

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Kodiyalam, V., Sunder, V.S. The planar algebra of a semisimple and cosemisimple Hopf algebra. Proc. Indian Acad. Sci. (Math. Sci.) 116, 443–458 (2006). https://doi.org/10.1007/BF02829702

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