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On Nichols algebras over basic Hopf algebras
2018This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field $\Bbbk$ of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is basic is a lifting of a Nichols algebra of a semisimple Yetter-Drinfeld module and we explain how to classify Nichols algebras
Andruskiewitsch, Nicol��s +1 more
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An Introduction to Nichols Algebras
2017Nichols algebras, Hopf algebras in braided categories with distinguished properties, were discovered several times. They appeared for the first time in the thesis of W. Nichols [72], aimed to construct new examples of Hopf algebras. In this same paper, the small quantum group \(u_q(sl_3)\), with q a primitive cubic root of one, was introduced ...
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EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2
Journal of Algebra and Its Applications, 2013We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1and A1× A1with the order NJ> 2 for at least one component J, are wild.
Yu, Xiaolan, Zhang, Yinhuo
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Orbifoldizing Hopf- and Nichols-Algebras
2012The main goal of this thesis is to explore a new general construction of orbifoldizing Hopf- and Nicholsalgebras, describe the growth of the automorphism group and compare the behaviour of certain associated categories to Kirillov's orbifoldizing. Together with outlooks towards vertex algebras these aspects form the 5-fold subdivision of this thesis ...
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Nichols algebras of group type with many quadratic relations
Advances in Mathematics, 2011Leandro Vendramin
exaly
Quantum groups and Nichols algebras acting on conformal field theories
Advances in Mathematics, 2021exaly