Isomorphism classes and automorphisms of finite Hopf algebras of type A_n

2005/11/10 by Nicol/'as Andruskiewitsch, Hans-Jürgen Schneider, Andruskiewitsch, Nicol/'as +1
Mathematics · #16W30 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0511283

25 pages. The second version is final, to appear in Proceedings of the XVI Coloquio Latinoamericano de Algebra (Colonia, Uruguay, 2005)

arxiv created 2007/02/19 · arxiv updated 2009/12/01

Abstract

In our previous paper math/0502157 we classified a large class of finite-dimensional pointed Hopf algebras up to isomorphism. However the following problem was left open for Hopf algebras of of type A,D or E₆, that is whose Cartan matrix is connected and allows a non-trivial automorphism of the corresponding Dynkin diagram. In this case we described the isomorphisms between two such Hopf algebras with the same Cartan matrix only implicitly. The problem is whether it is possible to compute the isomorphisms in terms of the defining families of parameters. In the present paper we solve this problem for type A.

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