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Modules, comodules and cotensor products over Frobenius algebras

Summary: Modules, comodules and cotensor products
over Frobenius algebras
Lowell Abrams
Department of Mathematics
Rutgers University
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


Source: Abrams, Lowell - Department of Mathematics, George Washington University


Collections: Mathematics