The Brauer group of Sweedler’s Hopf algebra 𝐻₄

DOI10.1090/S0002-9939-00-05628-8zbMath0964.16036OpenAlexW2162209988MaRDI QIDQ4517473

Yinhuo Zhang, Freddy M. J. van Oystaeyen

Publication date: 22 November 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05628-8

zbMATH Keywords

group-like elementsHopf algebrasBrauer groupssplit exact sequencesskew-primitive elementsBrauer-Wall groupsAzumaya algebrasquasi-triangular structures

Mathematics Subject Classification ID

Related Items (15)

COMPUTING SUBGROUPS OF THE BRAUER GROUP OFH₄ ⋮ Structure theorems of \(H_4\)-Azumaya algebras. ⋮ The Brauer group of modified supergroup algebras. ⋮ Villamayor-Zelinsky sequence for symmetric finite tensor categories ⋮ On the subgroup structure of the full Brauer group of Sweedler Hopf algebra. ⋮ An exact sequence for the Brauer group of a finite quantum group. ⋮ A sequence to compute the Brauer group of certain quasi-triangular Hopf algebras. ⋮ Four-dimensional Yetter-Drinfeld module algebras over \(H_4\). ⋮ Cocycle twisting of \(E(n)\)-module algebras and applications to the Brauer group. ⋮ When is a cleft extension \(H\)-Azumaya? ⋮ Classification of 4-Dimensional Graded Algebras ⋮ Group gradings and actions of pointed Hopf algebras ⋮ Cocycle Deformations and Brauer Groups ⋮ Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras. ⋮ The Brauer group of some quasitriangular Hopf algebras.

Cites Work

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• Coalgebra actions on Azumaya algebras
• Algebraic aspects of the quantum Yang-Baxter equation
• The Brauer group of a braided monoidal category
• Quantum Yang-Baxter module algebras
• Quantum groups and representations of monoidal categories
• Crossed Products and Inner Actions of Hopf Algebras
• Embedding the Hopf Automorphism Group into the Brauer Group
• The Brauer group of Yetter-Drinfel’d module algebras
• Quaternion algebras and hopf crossed products
• Graded Brauer Groups.

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