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arXiv · 2512.23074

Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras

Bouzid Mosbahi·Imed Basdouri·Jean Lerbet
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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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Bouzid Mosbahi, Imed Basdouri, Jean Lerbet. 2025-12-28. Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras. https://arxiv.org/abs/2512.23074

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