Finite quantum groups over abelian groups of prime exponent

By N. Andruskiewitsch, Hans Jürgen Schneider. 2000

73 citations recorded by the source corpus.

Abstract We classify pointed finite-dimensional complex Hopf algebras whose group of group-like elements is abelian of prime exponent p, p>17. The Hopf algebras we find are members of a general family of pointed Hopf algebras we construct from Dynkin diagrams. As special cases of our construction we obtain all the Frobenius–Lusztig kernels of semisimple Lie algebras and their parabolic subalgebras. An important step in the classification result is to show that all these Hopf algebras are generated by group-like and skew-primitive elements.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8986926aef463e45e4eff95f37dfbd4ffc073a26

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In Algebra and Number Theory

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Citations in the corpus

Hopf Algebras and Root Systems (2020, methodology): “Several years after their discovery, general classiﬁcation results for pointed Hopf algebras were obtained ([ AS02 ]; [ AS04 ], [ AA08 ], [ AS10 ] depending on [ Ros98 ], [ Kha99 ], [ Hec06 ], [ Hec08 ]).”
Basic quasi-Hopf algebras over cyclic groups (2009, background): “Hˆ H ! Aˆ = A(H,ωˆ s) /// QQQ(((( QQQQQ QQQQQ QQ A1 = A(H1,ωs) vmvvmvmm mmmmm mmmm A¯ = A(H,ω¯ s) ooo A. Call K(V) the subalgebra generated by the xNI α in Be(V): by Proposition 4.7 in [AS3], it is a braided Hopf subalgebra of Be(V). In consequence, by twisting and restriction, the algebra K gene”
Liftings of Nichols algebras of diagonal type II: all liftings are cocycle deformations (2016, methodology): “uch that gru(λ)≃B(V)#H. 1. Introduction The program for the classiﬁcation of ﬁnite-dimensional pointed Hopf algebra with abelian coradical kΓ was initiated by N. Andruskiewitsch and H.J. Schneider in [AS1], where they proposed a lifting method to deal with this problem. The method proved to be very ”