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Duality and Rational Modules in Hopf Algebras over Commutative Rings

✍ Scribed by J.Y Abuhlail; J Gómez-Torrecillas; F.J Lobillo

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 155 KB
Volume: 240
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8722

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✦ Synopsis

Let A be an algebra over a commutative ring R. If R is noetherian and A • is pure in R A , then the categories of rational left A-modules and right A • -comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A • in R A .

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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 ring