偏Doi-Hopf群结构

Structures of Partial Doi-Hopf Group

通过引入偏Doi-Hopf群结构和偏Doi-Hopf群模的概念,推广了Doi-Hopf结构,并给出其应用实例和基本的代数性质.综合群余代数和偏缠绕结构的思想构造了从偏Doi-Hopf群模范畴到模范畴的忘却函子,并证明了它有右伴随函子.

We first introduced the notions of partial Doi-Hopf group structures and partial Doi-Hopf group modules which generalize Doi-Hopf structures and Doi-Hopf modules. Then we gave some examples and basic properties. Mainly we combined the idea of group coalgebras with partial entwining structures to construct the forgetful funetor from the category of partial Doi-Hopf group modules to that of modules and proved that it has a right adjoint funetor.