Relative Hopf Modules for (Dual) Quasi-Hopf Algebras
نویسندگان
چکیده
منابع مشابه
Two-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...
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A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...
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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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We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by YetterDrinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new c...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8279