Hochschild–Mitchell cohomology and Galois extensions
Copyright policy )Hochschild–Mitchell cohomology and Galois extensions
We define $H$-Galois extensions for $k$-linear categories and a Hopf algebra $H$ 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 $H$ a group algebra decomposes as a direct sum indexed by the set of conjugacy classes of the group. We also compute some Hochschild-Mitchell cohomology groups of categories with infinite associated quiver.
21 pages
- National Scientific and Technical Research Council Argentina
- Facultad de Ciencias Agrarias y Forestales Argentina
- Universidid De Buenos Aires Argentina
- University of Buenos Aires Argentina
Hochschild cohomology, 16W50; 18E05; 16W30; 16S40; 16D90, Galois extensions, 16D90, FOS: Mathematics, https://purl.org/becyt/ford/1.1, 16S40, https://purl.org/becyt/ford/1, Hopf algebra actions, 18E05, Algebra and Number Theory, Smash products of general Hopf actions, Preadditive, additive categories, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, small linear categories, Hopf algebras (associative rings and algebras), Spectral sequences, hypercohomology, Hopf algebras, spectral sequences, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Mathematics - K-Theory and Homology, 16W30, 16W50
Hochschild cohomology, 16W50; 18E05; 16W30; 16S40; 16D90, Galois extensions, 16D90, FOS: Mathematics, https://purl.org/becyt/ford/1.1, 16S40, https://purl.org/becyt/ford/1, Hopf algebra actions, 18E05, Algebra and Number Theory, Smash products of general Hopf actions, Preadditive, additive categories, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, small linear categories, Hopf algebras (associative rings and algebras), Spectral sequences, hypercohomology, Hopf algebras, spectral sequences, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Mathematics - K-Theory and Homology, 16W30, 16W50
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