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

TL;DR

This paper investigates the cohomology, deformations, and operator structures of Hom-Leibniz conformal algebras, introducing Hom-NS-Leibniz conformal algebras and analyzing their properties and applications.

Contribution

It defines cohomologies for Hom-Leibniz conformal and Nijenhuis operators, and introduces Hom-NS-Leibniz conformal algebras with operator-based constructions.

Findings

Cohomologies for Hom-Leibniz conformal and Nijenhuis operators are determined.

Formal deformations of Nijenhuis operators are studied.

Hom-NS-Leibniz conformal algebras are constructed using various operators.

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.