Cohomological aspects of Hopf algebra liftings

2009/09/23 by Grunenfelder, L.
#16T05 #18G50 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0909.4112

Abstract

A recent result of ours [GM] shows that all Hopf algebra liftings of a given diagram in the sense of Andruskiewitsch and Schneider are cocycle deformations of each other. Here we develop a "non-abelian" cohomology theory, which gives a method for an explicit description of cocycles relevant to the lifting process.

Related

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• Lifting via cocycle deformation
• Homotopy lifting maps on Hochschild cohomology and connections to deformation of algebras using reduction systems
• Pointed and copointed Hopf algebras as cocycle deformations
• Liftings of Nichols algebras of diagonal type II. All liftings are\n cocycle deformations