Summary: Modules, comodules and cotensor products
over Frobenius algebras
Department of Mathematics
New Brunswick, NJ 08903
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 of right (left) comodules over A, relative to
this coproduct, is isomorphic to the 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 M2N of a right Amodule M
and a left Amodule N is isomorphic to the vector space of homomor
phisms from a particular left A e module D to
N# 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 M2N and