Year: 2024
Author: Zhangju Liu, Yunhe Sheng
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 30–42
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 $gl(V)⊕V.$ 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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0019
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 30–42
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Leibniz algebra omni-Lie algebra representation cohomology.