Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras

2025/12/28 by Mosbahi, Bouzid, Basdouri, Imed, Lerbet, Jean
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.23074

Abstract

In this paper, we introduce and study Reynolds--Nijenhuis operators on associative algebras a novel hybrid structure that simultaneously satisfies the defining identities of both Reynolds and Nijenhuis operators. We investigate their connections with Rota-Baxter and modified Rota-Baxter operators. We develop a representation theory for Reynolds--Nijenhuis associative algebras and introduce a corresponding cohomology theory. Furthermore, we establish a one-parameter formal deformation theory for these algebras, examining the role of infinitesimals, rigidity, and equivalence in the context of deformations.

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Related

• Nijenhuis operators on Leibniz algebras
• Deformations and homotopy theory of Nijenhuis associative algebras
• Deformation maps of Quasi-twilled associative algebras
• Deformations of associative Rota-Baxter operators
• Cohomology theory of Nijenhuis family Ω-associative algebras