Omni-representations of Leibniz algebras

Zhangju Liu; Yunhe Sheng

Omni-representations of Leibniz algebras

Rings and Algebras 2024-03-25 v1 Representation Theory

Authors: Zhangju Liu , Yunhe Sheng

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.

Keywords

leibniz algebras omni-representations omni-lie algebra omni-cohomology loday-pirashvili cohomology

Cite

@article{arxiv.2304.02809,
  title  = {Omni-representations of Leibniz algebras},
  author = {Zhangju Liu and Yunhe Sheng},
  journal= {arXiv preprint arXiv:2304.02809},
  year   = {2024}
}

Comments

11 pages. arXiv admin note: substantial text overlap with arXiv:1408.2225

Omni-representations of Leibniz algebras

Abstract

Keywords

Cite

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