Cohomology and deformation theory of Averaging Leibniz algebras

2025/12/10 by Bouzid Mosbahi, Mosbahi, Bouzid, Imed Basdouri +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2512.09328

openalex publication_date 2025/12/10 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation theories of averaging Leibniz algebras, showing that the cohomology we define is closely connected to deformation cohomology.

Citations

• Quasi-Centroids and Quasi-Derivations of low-dimensional Zinbiel algebras
• On structures of BiHom-Superdialgebras and their derivations
• Averaging operators on groups, racks and Leibniz algebras
• Nijenhuis operators on Leibniz algebras
• On BiHom-associative dialgebras
• Leibniz algebras with derivations
• Classification of 3-Dimensional BiHom-Associative and BiHom-Bialgebras
• Structure and classification of Hom-associative algebras
• An Algebraic Study of Averaging Operators
• On some structures of Leibniz algebras
• Classification of 4-dimensional nilpotent complex Leibniz algebras
• Universal enveloping algebras of Leibniz algebras and (co)homology

Cited by

• Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras

Related

• Cohomology and Deformation of Leibniz Superalgebras
• Cohomology theory of averaging algebras, L_∞-structures and homotopy averaging algebras
• Controlling structures, deformations and homotopy theory for averaging algebras
• Deformation maps in proto-twilled Leibniz algebras
• Nijenhuis operators on Leibniz algebras