✦ LIBER ✦

On Hopf Algebras with Positive Bases

✍ Scribed by Jiang-Hua Lu; Min Yan; Yongchang Zhu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 170 KB
Volume: 237
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8459

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✦ Synopsis

We show that if a finite dimensional Hopf algebra H over ‫ރ‬ has a basis with respect to which all the structure constants are nonnegative, then H is isomorphic to the bi-cross-product Hopf algebra constructed by Takeuchi and Majid from a finite group G and a unique factorization G s G G of G into two subgroups.

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We also show that Hopf algebras in the category of finite sets with correspondences as morphisms are classified in a similar way. Our results can be used to explain some results on Hopf algebras from the set-theoretical point of view.

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