Omni-representations of Leibniz algebras

Commun. Math. Res. 40 (2024), No. 1, 30-42 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 associa...

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Hauptverfasser:	Liu, Zhangju, Sheng, Yunhe
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Representation Theory Mathematics - Rings and Algebras
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Zusammenfassung:	Commun. Math. Res. 40 (2024), No. 1, 30-42 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.
DOI:	10.48550/arxiv.2304.02809