Quadratic Lie Algebras
Quantum Algebra
2009-06-26 v1 Rings and Algebras
Abstract
In this paper, the notion of universal enveloping algebra introduced in [A. Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected Braided Bialgebras}, submitted. (arXiv:0805.3391v3)] is specialized to the case of braided vector spaces whose Nichols algebra is quadratic as an algebra. In this setting a classification of universal enveloping algebras for braided vector spaces of dimension not greater than 2 is handled. As an application, we investigate the structure of primitively generated connected braided bialgebras whose braided vector space of primitive elements forms a Nichols algebra which is quadratic algebra.
Cite
@article{arxiv.0906.4617,
title = {Quadratic Lie Algebras},
author = {Alessandro Ardizzoni and Fabio Stumbo},
journal= {arXiv preprint arXiv:0906.4617},
year = {2009}
}