Computational Methods for Rota-type operators on 4-dimensionnal nilpotent Leibniz Algebras

2025/04/27 by Abdou, Ahmed Zahari, Gamou, Kol Béatrice, Bakayoko, Ibrahima
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2504.19206

Abstract

A compatible nilpotent Leibniz algebra is a vector space equipped with two multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimensions less than four, as well as the classifications of their corresponding Rota-type operators.

Citations

• Structure and classification of Hom-associative algebras
• Deformation quantization of Leibniz algebras
• Rota-Baxter Hom-Lie-admissible algebras
• Splitting of operations, Manin products and Rota-Baxter operators
• Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2n-ary Graded and Homotopy Algebras
• Classification of 4-dimensional nilpotent complex Leibniz algebras
• Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem
• An analytic problem whose solution follows from a simple algebraic identity

Related

• Classification of 4-dimensional nilpotent complex Leibniz algebras
• The classification of 4-dimensional Leibniz algebras
• Classification of some operators on compatible ternary Leibniz algebras
• The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras
• Classification of three-dimensional Nijenhuis Leibniz algebras