On Nichols algebras with standard braiding

Details On Nichols algebras with standard braiding On Nichols algebras with standard braiding

2008-04-04

arxiv.org/abs/0804.0816v1

Algebra & Number Theory, Vol. 3 (2009), No. 1, 35-106

Mathematics

Quantum Algebra

70 pages

Scientific paper

The class of standard braided vector spaces, introduced by Andruskiewitsch and the author in \texttt{arXiv:math/0703924v2} to understand the proof of a theorem of Heckenberger \cite{H2}, 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.

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