TY - JOUR
T1 - A note on "Modules, Comodules, and Cotensor Products over Frobenius Algebras"
AU - Chen, Xiaowu
AU - Huang, Hualin
AU - Wang, Yanhua
PY - 2006/8
Y1 - 2006/8
N2 - 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.
AB - 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.
KW - Cotensor
KW - Frobenius coordinates
KW - Hochschild cohomology
UR - http://www.scopus.com/inward/record.url?scp=33747474082&partnerID=8YFLogxK
U2 - 10.1007/s11401-005-0025-z
DO - 10.1007/s11401-005-0025-z
M3 - Article
AN - SCOPUS:33747474082
SN - 0252-9599
VL - 27
SP - 419
EP - 424
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
IS - 4
ER -