Exploring Cohomology, Deformations, and Hom-NS Structures in Hom-Leibniz Conformal Algebras through Nijenhuis Operators

2024/12/29 by Sania Asif, Asif, Sania · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2412.20428

Abstract

This paper studies the Nijenhuis operator on Hom-Leibniz conformal algebra, defining their representations and cohomologies. We determine the cohomologies for both Hom-Leibniz conformal algebra and Nijenhuis operators on Hom-Leibniz conformal algebra. Subsequently, establishing the cohomology of Hom-Nijenhuis-Leibniz conformal algebras. As an application to this cohomology, we study formal deformations of the Nijenhuis operator on Hom-Leibniz conformal algebra. Additionally, we introduce Hom-NS-Leibniz conformal algebra and explore how various operators such as Rota-Baxter operator, Twisted Rota Baxter operator, and Nijenhuis operators can provide Hom-NS-Leibniz conformal algebras.

Cited by

• Quasi-Twilled Lie Pseudolgebras and Their Deformation Maps

Related

• Nijenhuis operators on Leibniz algebras
• Cohomology and deformation of compatible Hom-Leibniz algebras
• O-operators and Nijenhius operators of associative conformal algebras
• Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras
• Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras