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arXiv · 1607.05973

Universal enveloping algebras and Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras

Li Guo·Bin Zhang·Shanghua Zheng
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Abstract

A Hom-type algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative algebra on a Hom-module. We then apply this construction to obtain the universal enveloping algebra of an involutive Hom-Lie algebra. Finally we obtain a Poincar\'e-Birkhoff-Witt theorem for the enveloping associative algebra of an involutive Hom-Lie algebra.

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BibTeXRIS

Li Guo, Bin Zhang, Shanghua Zheng. 2016-07-20. Universal enveloping algebras and Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras. https://arxiv.org/abs/1607.05973

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