Bi-Galois objects over the Taft algebras

DOI10.1007/BF02810582zbMath0949.16040MaRDI QIDQ1972373

Peter Schauenburg

Publication date: 28 November 2000

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

group-like elementstensor productsskew-primitive elementsTaft algebrasHopf-Galois extensionscleft extensionsTaft Hopf algebrasbi-Galois objects

Mathematics Subject Classification ID

Related Items (18)

On the monoidal invariance of the cohomological dimension of Hopf algebras ⋮ Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension. ⋮ On the classification of Galois objects over the quantum group of a nondegenerate bilinear form. ⋮ Classifying bicrossed products of two Taft algebras ⋮ Extensions of the category of comodules of the Taft algebra ⋮ Quantum torsors ⋮ Invertible bimodule categories over the representation category of a Hopf algebra ⋮ A Hopf bundle over a quantum four-sphere from the symplectic group ⋮ Green rings of pointed rank one Hopf algebras of nilpotent type. ⋮ The group of braided autoequivalences of the category of comodules over a coquasi-triangular Hopf algebra ⋮ On the trace of the antipode and higher indicators. ⋮ THE HOPF AUTOMORPHISM GROUP AND THE QUANTUM BRAUER GROUP IN BRAIDED MONOIDAL CATEGORIES ⋮ A locally trivial quantum Hopf fibration. ⋮ Gauge groups and bialgebroids ⋮ THE GROUP OF BI-GALOIS OBJECTS OVER THE COORDINATE ALGEBRA OF THE FROBENIUS–LUSZTIG KERNEL OF SL(2) ⋮ GALOIS AND BIGALOIS OBJECTS OVER MONOMIAL NON-SEMISIMPLE HOPF ALGEBRAS ⋮ Galois objects over generalized Drinfeld doubles, with an application to \(u_q({\mathfrak sl}_2)\) ⋮ Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras.

Cites Work

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• Principal homogeneous spaces for arbitrary Hopf algebras
• Galois theories and normal bases
• Galois algebras and Harrison cohomology
• Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules
• Galois correspondences for Hopf bigalois extensions
• Hopf algebras and Galois theory
• Cleft extensions for a hopf algebra generated by a nearly primitive element
• Multiplication alteration by two-cocycles - the quantum version
• Braided bialgebras and quadratic blalgebras
• Hopf bigalois extensions
• Indecomposable Coalgebras, Simple Comodules, and Pointed Hopf Algebras
• Hopf-galois theory and tensor products of hopf algebras
• Abelian extensions of commutative rings
• The Order of the Antipode of Finite-dimensional Hopf Algebra

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