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Volume 40, Issue 1
Omni-Representations of Leibniz Algebras

Zhangju Liu & Yunhe Sheng

DOI: 10.4208/cmr.2023-0019

Commun. Math. Res., 40 (2024), pp. 30-42.

Published online: 2023-12

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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 $gl(V)⊕V.$ 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 algebra, omni-Lie algebra, representation, cohomology.

  • AMS Subject Headings

17B99, 17B10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-30, author = {Liu , Zhangju and Sheng , Yunhe}, title = {Omni-Representations of Leibniz Algebras}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {40}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0019}, url = {http://global-sci.org/intro/article_detail/cmr/22280.html} }
TY - JOUR T1 - Omni-Representations of Leibniz Algebras AU - Liu , Zhangju AU - Sheng , Yunhe JO - Communications in Mathematical Research VL - 1 SP - 30 EP - 42 PY - 2023 DA - 2023/12 SN - 40 DO - http://doi.org/10.4208/cmr.2023-0019 UR - https://global-sci.org/intro/article_detail/cmr/22280.html KW - Leibniz algebra, omni-Lie algebra, representation, cohomology. AB -

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.

Zhangju Liu & Yunhe Sheng. (2023). Omni-Representations of Leibniz Algebras. Communications in Mathematical Research . 40 (1). 30-42. doi:10.4208/cmr.2023-0019
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