Hopf–Galois extensions and an exact sequence for H-Picard groups
Copyright policy )Hopf–Galois extensions and an exact sequence for H-Picard groups
Let $H$ be a Hopf algebra, and $A$ an $H$-Galois extension. We investigate $H$-Morita autoequivalences of $A$, introduce the concept of $H$-Picard group, and we establish an exact sequence linking the $H$-Picard group of $A$ and the Picard group of $A^{{\rm co}H}$.
35 pages; to appear in J. Algebra
- Babeș-Bolyai University Romania
- VRIJE UNIVERSITEIT BRUSSEL Belgium
- Vrije Universiteit Brussel Belgium
cleft extension, Algebra and Number Theory, Hopf algebras and their applications, Picard groups, Morita equivalence, Hopf Galois extensions, Actions of groups and semigroups; invariant theory (associative rings and algebras), Morita equivalences, Hopf–Galois extension, Mathematics - Rings and Algebras, Sweedler cohomology, Cleft extension, cleft extensions, Module categories in associative algebras, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Hopf-Galois extension, 16D90, FOS: Mathematics, Picard group, 16W30, 16W30; 16D90
cleft extension, Algebra and Number Theory, Hopf algebras and their applications, Picard groups, Morita equivalence, Hopf Galois extensions, Actions of groups and semigroups; invariant theory (associative rings and algebras), Morita equivalences, Hopf–Galois extension, Mathematics - Rings and Algebras, Sweedler cohomology, Cleft extension, cleft extensions, Module categories in associative algebras, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Hopf-Galois extension, 16D90, FOS: Mathematics, Picard group, 16W30, 16W30; 16D90
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