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September 10, 2025Open Access

On n-Hom-pre-Lie color algebras and associated Kupershmidt operators

Key Points

n-Hom-pre-Lie color algebras extend traditional n-pre-Lie algebras, enriching their structure and applications.
Key results include the integration of Rota-Baxter and Kupershmidt operators, enhancing understanding in algebraic frameworks.
The construction of induced n-Hom-pre-Lie color algebras demonstrates the versatility and potential of these new algebraic structures.
Applications of these theories could lead to advancements in mathematical physics and computational algebra.

Abstract

In this paper, we introduce the Hom-color generalization of n-pre-Lie algebras called n-Hom-pre-Lie color algebras in which, we investigate their representation theory and we give some related results and structures based on Rota-Baxter operators, Kupershmidt operators and Nijenhuis operators. Moreover, we show that given (n-2)-linear form of a Hom-pre-Lie color algebra satisfying certain conditions, one can construct a structure of n-Hom-pre-Lie color algebra called induced n-Hom-pre-Lie color algebra. The same procedure is applied for the representation of n-Hom-pre-Lie color algebras.

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