Summary: Dual Entwining Structures and Dual Entwined
Jawad Y. Abuhlail
P.O. Box 14, Birzeit - Palestine
In this note we introduce and investigate the concepts of dual entwining structures
and dual entwined modules. This generalizes the concepts of dual Doi-Koppinen
structures and dual Doi-Koppinen modules introduced (in the infinite case over rings)
by the author is his dissertation.
This note deals with the following problem: let (A, C, ) be a given entwining structure over
a commutative base ring R. Find an R-subalgebra A C
and an R-coalgebra C A
such that (A, C,
) is an entwining structure.
For general entwining structures, it's not clear if such a dual entwining structure exists.
However, once it's found, we have the expected duality theorems between the corresponding