Induction functors and stable Clifford theory for Hopf modules
نویسندگان
چکیده
منابع مشابه
Hopf Pairings and Induction Functors over Rings
The so called induction functors appear in several areas of Algebra in different forms. Interesting examples are the induction functors in the Theory of Affine Algebraic groups. In this note we investigate the so called Hopf pairings (bialgebra pairings) and use them to study induction functors for affine group schemes over arbitrary commutative ground rings. We present also a special type of H...
متن کاملSeparable Functors for the Category of Doi-hopf Modules. Applications
We prove a Maschke type Theorem for the category of Doi-Hopf modules. In fact, we give necessary and sufficient conditions for the functor forgetting the C-coaction to be separable. This leads to a generalized notion of integrals. Our results can be applied to obtain Maschke type Theorems for Yetter-Drinfel’d modules, Long dimodules and modules graded by G-sets. Existing Maschke type Theorems d...
متن کاملClifford Modules and Twisted K-theory
The setting is the following: V is a real vector bundle on a compact space X, provided with a non degenerate quadratic form to which we associate a bundle of (real or complex) Clifford algebras denoted by C(V ); the quadratic form is implicit in this notation. We denote by M(V ) the Grothendieck group associated to the category of (real or complex) vector bundles provided with a structure of (t...
متن کاملHopf Pairings and (Co)induction Functors over Commutative Rings
Co)induction functors appear in several areas of Algebra in different forms. Interesting examples are the so called induction functors in the Theory of Affine Algebraic Groups. In this paper we investigate Hopf pairings (bialgebra pairings) and use them to study (co)induction functors for affine group schemes over arbitrary commutative ground rings. We present also a special type of Hopf pairin...
متن کاملStable Clifford Theory for Divisorially Graded Rings
Dade [D1, Theorem 7.4] obtained an important result on the equivalence of categories, extending the classical stable Clifford theory. He used the theory of strongly graded rings. Recently, this work has been generalized to arbitrary graded rings, see E. Dade [D2], [D3], J.L. Gómez Pardo and C. Nǎstǎsescu [GN ], C. Nǎstǎsescu and F. Van Oystaeyen [NVO2]. In the classical case the stable Clifford...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1996
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)00073-9