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On Antipodes and Integrals in Hopf Algebras over Rings and the Quantum Yang-Baxter Equation

✍ Scribed by K.I. Beidar; Y. Fong; A.A. Stolin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 240 KB
Volume: 194
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.7019

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✦ Synopsis

The authors showed previously on Frobenius algebras and quantum Yang-Baxter . equation, II, preprint, TRITA-MAT-1995, February 1995 that every Frobenius algebra over a commutative ring defines a solution of the quantum Yang-Baxter equation. Applying this result to Hopf algebras over commutative rings which are finitely generated and projective as modules, we obtain an explicit formula for this solution. It turns out that this solution can be expressed in terms of the integral and antipode. We use this solution to characterize separable Hopf algebras over rings. Some results on the order of the antipode are also obtained. ᮊ 1997 Aca- demic Press

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