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Hochschild-Mitchell cohomology and Galois extensions. (English) Zbl 1118.16012

The paper extends some classical results on Hochschild cohomology of rings to Hochschild cohomology of small linear categories. Such categories arise in the study of Galois coverings of quivers. The authors construct a spectral sequence in the context when a Hopf algebra acts on a linear category. The spectral sequence generalizes the one constructed by C. Cibils and M. J. Redondo [J. Algebra 284, No. 1, 310-325 (2005; Zbl 1065.18010)]. In the case when the Hopf algebra is a group algebra of a finite group \(G\) the spectral sequence splits as a sum of spectral sequences indexed by the conjugacy classes of \(G\).

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
18E05 Preadditive, additive categories
18G40 Spectral sequences, hypercohomology
16S40 Smash products of general Hopf actions
16W30 Hopf algebras (associative rings and algebras) (MSC2000)

Citations:

Zbl 1065.18010
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References:

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