by Andruskiewitsch, Nicolás; Dăscălescu, Sorin

This is a contribution to the classification of finite-dimensional pointed Hopf algebras. We are concerned with the case when the group of group-like elements is Abelian of exponent 2. We attach to such a pointed Hopf algebra a generalized simply-laced Cartan matrix; we conjecture that the Hopf algebra is finite-dimensional if and only if the Cartan matrix is of finite type. We prove the conjecture for the types An and An(1). We obtain the classification of all possible Hopf algebras with Cartan matrix An. We use the lifting method developed by Hans-Jürgen Schneider and the first-named author.

DOI: 10.1007/s10468-004-6008-z
Print publication date: 3/1/2005
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