Pointed Hopf algebras as cocycle deformations

2010/10/24 by L. Grünenfelder, Grunenfelder, L., Mitja Mastnak +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1010.4976

Abstract

We show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of each other. This is done by giving first a suitable characterization of such Hopf algebras, which allows for the application of results by Masuoka about Morita-Takeuchi equivalence and by Schauenburg about Hopf Galois extensions. We also outline a method to describe the deforming cocycles involved using the exponential map and its q-analogue.

Cited by

• Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra
• Cohomology and Coquasi-bialgebras in the category of Yetter-Drinfeld\n Modules
• Cocycle deformations for liftings of quantum linear spaces

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