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| A Note on "Modules, Comodules, and Cotensor Products over Frobenius Algebras" |
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Citation： |
Xiaowu CHEN,Hualin HUANG,Yanhua WANG.A Note on "Modules, Comodules, and Cotensor Products over Frobenius Algebras"[J].Chinese Annals of Mathematics B,2006,27(4):419~424 |
| Page view： 1285
Net amount： 1149 |
Authors： |
Xiaowu CHEN; Hualin HUANG;Yanhua WANG |
Foundation： |
Project supported by AsiaLink Project "Algebras and Representations in China and Europe" ASI/B7-
301/98/679-11 and the National Natural Science Foundation of China (No.10271113). |
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| Abstract： |
This is a note on Abrams' paper "Modules, Comodules, and Cotensor
Products over Frobenius Algebras, Journal of Algebras" (1999).
With the application of Frobenius coordinates developed recently
by Kadison, one has a direct proof of Abrams' characterization for
Frobenius algebras in terms of comultiplication (see L. Kadison
(1999)). For any Frobenius algebra, by using the explicit
comultiplication, the explicit correspondence between the category
of modules and the category of comodules is obtained. Moreover,
with this we give very simplified proofs and improve Abrams'
results on the Hom functor description of cotensor functor. |
Keywords： |
Frobenius coordinates, Cotensor, Hochschild cohomology |
Classification： |
17A60, 18G15 |
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