Omni-Representations of Leibniz Algebras

Omni-Representations of Leibniz Algebras

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.

Author Details

Zhangju Liu

Yunhe Sheng

  1. Symplectic structures, product structures and complex structures on Leibniz algebras

    Tang, Rong

    Xu, Nanyan

    Sheng, Yunhe

    Journal of Algebra, Vol. 647 (2024), Iss. P.710

    https://doi.org/10.1016/j.jalgebra.2024.03.003 [Citations: 0]