# Quadratic Lie Algebras - Mathematics > Quantum Algebra

Abstract: In this paper, the notion of universal enveloping algebra introduced in A.Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected BraidedBialgebras}, submitted. arXiv:0805.3391v3 is specialized to the case ofbraided vector spaces whose Nichols algebra is quadratic as an algebra. In thissetting a classification of universal enveloping algebras for braided vectorspaces of dimension not greater than 2 is handled. As an application, weinvestigate the structure of primitively generated connected braided bialgebraswhose braided vector space of primitive elements forms a Nichols algebra whichis quadratic algebra.

Author: Alessandro Ardizzoni, Fabio Stumbo

Source: https://arxiv.org/