Cohomology and deformation theory of Averaging Leibniz algebras
Bouzid Mosbahi, Imed Basdouri, Jean Lerbet
TL;DR
This paper develops a cohomology theory for averaging Leibniz algebras, introduces representations, and explores their deformation theories, linking cohomology to algebraic deformations.
Contribution
It introduces the concepts of representation and dual representation for averaging Leibniz algebras and develops their associated cohomology and deformation theories.
Findings
Cohomology theory for averaging Leibniz algebras established
Connections between cohomology and deformation theory demonstrated
Framework for infinitesimal and formal deformations provided
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Geometry Research