Hochschild cohomology on Hopf Galois extensions
نویسندگان
چکیده
منابع مشابه
Hochschild-Mitchell cohomology and Galois extensions
We define H-Galois extensions for k-linear categories and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology related to this situation. This spectral sequence is multiplicative and for a group algebra decomposes as a direct sum indexed by conjugacy classes of the group. We also compute some Hochschild-Mitchell cohomology groups of categories with infinite...
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Let B ⊆ A be an H-Galois extension. If M is a Hopf bimodule then HH∗(A, M), the Hochschild homology of A with coefficients in M , is a right comodule over the coalgebra CH = H/[H,H]. Given an injective left CHcomodule V , our aim is to investigate the relationship between HH∗(A, M) CHV and HH∗(B, M CHV ). The roots of this problem can be found in [Lo2], where HH∗(A,A) G and HH∗(B,B) are shown t...
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is an isomorphism, which can be interpreted as the correct algebraic formulation of the condition that the G-action of X should be free, and transitive on the fibers of the map X → Y . In many applications surjectivity of the Galois map β, which, in the commutative case, means freeness of the action of G, is obvious, or at least easy to prove (it is sufficient to find 1 ⊗ h in the image for eac...
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In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A H to each twisted algebra H obtained from a Hopf algebra H by twisting its product with the help of a cocycle α. The algebra A H is a flat deformation of H over a “big” central subalgebra B H and can be viewed as the noncommutative analogue of a versal torsor in the sense of Serre. After surveying the results...
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We continue the investigation of H-Galois extensions of linear categories, where H is a Hopf algebra. In our main result, the Theorem 2.2, we characterize this class of extensions in the case when H is finite dimensional. As an application, we prove a version of the Duality Theorem for crossed products with invertible cocycle. Introduction The duality theorems for actions and coactions originat...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1995
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)00101-2