Abstract

The class of standard braided vector spaces, introduced by Andruskiewitsch and the author in 2007 to understand the proof of a theorem of Heckenberger, is slightly more general than the class of braided vector spaces of Cartan type. In the present paper, we classify standard braided vector spaces with finite-dimensional Nichols algebra. For any such braided vector space, we give a PBW basis, a closed formula of the dimension and a presentation by generators and relations of the associated Nichols algebra.

Keywords

quantized enveloping algebras, Nichols algebras, automorphisms of noncommutative algebras, pointed Hopf algebras

Mathematical Subject Classification

Primary: 17B37

Secondary: 16W20, 16W30

Authors