Hopf algebras with triality
Rings and Algebras
2011-06-22 v1
Abstract
In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and Zavarnitsine to groups with triality.
Keywords
Cite
@article{arxiv.1106.4302,
title = {Hopf algebras with triality},
author = {Georgia Benkart and Sara Madariaga and José M. Pérez-Izquierdo},
journal= {arXiv preprint arXiv:1106.4302},
year = {2011}
}
Comments
AMS-LaTeX, 23 pages. To appear in Trans. Amer. Math. Soc