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 - <p style="text-align: justify;">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.</p>