Hopf algebras with triality

Benkart, Georgia; Madariaga, Sara; Pérez-Izquierdo, José

doi:10.1090/S0002-9947-2012-05656-X

Hopf algebras with triality
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by Georgia Benkart, Sara Madariaga and José M. Pérez-Izquierdo PDF

Trans. Amer. Math. Soc. 365 (2013), 1001-1023 Request permission

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.

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