An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗)

For a commutative ring R and a commutative cocommutative Hopf algebra H finitely generated projective as an R -module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group BD ( R ,  H ) of H -dimodule and the Brauer B D ( R , H ∗ ) of...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2023-06, Vol.64 (2), p.445-458
Main Author: Nango, Christophe Lopez
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Commutativity
Convex and Discrete Geometry
Geometry
Group theory
Isomorphism
Mathematics
Mathematics and Statistics
Original Paper
Rings (mathematics)
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Summary:For a commutative ring R and a commutative cocommutative Hopf algebra H finitely generated projective as an R -module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group BD ( R ,  H ) of H -dimodule and the Brauer B D ( R , H ∗ ) of H ∗ -dimodule algebras, where H ∗ is the linear dual of H . In this paper, we generalize this result by constructing an anti-isomorphism of groups between BD ( S ,  H ), the Brauer group of dyslectic ( S ,  H )-dimodule algebras and B D ( S op , H ∗ ) , the Brauer group of dyslectic ( S op , H ∗ ) -dimodule algebras, where S is an H -commutative H -dimodule algebra and S op is the opposite algebra of S .
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-022-00641-3