Omni-representations of Leibniz algebras

Zhangju Liu; Yunhe Sheng

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arXiv · 2304.02809

Omni-representations of Leibniz algebras

Zhangju Liu·Yunhe Sheng

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Abstract

In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.

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Zhangju Liu, Yunhe Sheng. 2023-04-06. Omni-representations of Leibniz algebras. https://arxiv.org/abs/2304.02809

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