Hopf algebras with triality

Details Hopf algebras with triality Hopf algebras with triality

2011-06-21

arxiv.org/abs/1106.4302v1

Mathematics

Rings and Algebras

AMS-LaTeX, 23 pages. To appear in Trans. Amer. Math. Soc

Scientific paper

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.

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