Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups

2024/11/04 by Andruskiewitsch, N., Heckenberger, I., Vendramin, L. · 3 citations
#16T05 #20F55 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2411.02304

Abstract

We classify finite-dimensional Nichols algebras of Yetter-Drinfeld modules with indecomposable support over finite solvable groups in characteristic 0, using a variety of methods including reduction to positive characteristic. As a consequence, all Nichols algebras over groups of odd order are of diagonal type, which allows us to describe all pointed Hopf algebras of odd dimension.

Cited by

• Subracks and second homology of the conjugacy classes of finite projective special linear groups of degree two
• Pointed Hopf algebras revisited, with a view from tensor categories
• Some classifications of finite-dimensional Hopf algebras over the Hopf algebra H_b:x²y of Kashina

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• On Nichols algebras of low dimension
• On pointed Hopf algebras over nilpotent groups
• Examples of finite-dimensional pointed Hopf algebras in positive characteristic
• On Nichols algebras over basic Hopf algebras
• The Nichols algebra of a semisimple Yetter-Drinfeld module