منابع مشابه
Doi-Hopf Modules over Weak Hopf Algebras
The theory of Doi-Hopf modules [7, 10] is generalized to Weak Hopf Algebras [1, 12, 2].
متن کاملTwo-sided (two-cosided) Hopf modules and Doi-Hopf modules for quasi-Hopf algebras
Let H be a finite dimensional quasi-Hopf algebra over a field k and A a right H-comodule algebra in the sense of [12]. We first show that on the k-vector space A⊗H∗ we can define an algebra structure, denoted by A # H∗, in the monoidal category of left H-modules (i.e. A # H∗ is an Hmodule algebra in the sense of [2]). Then we will prove that the category of two-sided (A,H)bimodules HM H A is is...
متن کاملDoi-Koppinen Hopf Modules Versus Entwined Modules
A Hopf module is an A-module for an algebra A as well as a C-comodule for a coalgebra C, satisfying a suitable compatibility condition between the module and comodule structures. To formulate the compatibility condition one needs some kind of interaction between A and C. The most classical case arises when A = C =: H is a bialgebra. Many subsequent variants of this were unified independently by...
متن کاملDuality and Rational Modules in Hopf Algebras over Commutative Rings
Let A be an algebra over a commutative ring R. If R is noetherian and A◦ is pure in R, then the categories of rational left A-modules and right A◦-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner– Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A◦ in R. © 2001 Academic Press
متن کاملHom-tensor Relations for Two-sided Hopf Modules over Quasi-hopf Algebras
For a Hopf algebra H over a commutative ring k, the category MH of right Hopf modules is equivalent to the category Mk of k-modules, that is, the comparison functor −⊗k H : Mk → MH is an equivalence (Fundamental theorem of Hopf modules). This was proved by Larson and Sweedler via the notion of coinvariants McoH for any M ∈ MH . The coinvariants functor (−) coH : MH → Mk is right adjoint to the ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2000
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870008827113