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Modules, Comodules, and Cotensor Products over Frobenius Algebras

✍ Scribed by Lowell Abrams

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 95 KB
Volume: 219
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7901

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✦ Synopsis

We characterize noncommutative Frobenius algebras A in terms of the existence of a coproduct which is a map of left A e -modules. We show that the category Ž . of right left comodules over A, relative to this coproduct, is isomorphic to the Ž . category of right left modules. This isomorphism enables a reformulation of the cotensor product of Eilenberg and Moore as a functor of modules rather than comodules.

We prove that the cotensor product M I N of a right A-module M and a left A-module N is isomorphic to the vector space of homomorphisms from a particular left A e -module D to N m M, viewed as a left A e -module. Some properties of D are described. Finally, we show that when A is a symmetric algebra, the cotensor product M I N and its derived functors are given by the Hochschild cohomology over A of N m M.

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