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arXiv · 1106.4302

Hopf algebras with triality

Georgia Benkart·Sara Madariaga·José M. Pérez-Izquierdo
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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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Georgia Benkart, Sara Madariaga, José M. Pérez-Izquierdo. 2011-06-21. Hopf algebras with triality. https://arxiv.org/abs/1106.4302

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