Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras

Fuente: arXiv
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Main Authors: Mosbahi, Bouzid, Basdouri, Imed, Lerbet, Jean
Format: Preprint
Published: 2025
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author Mosbahi, Bouzid
Basdouri, Imed
Lerbet, Jean
author_facet Mosbahi, Bouzid
Basdouri, Imed
Lerbet, Jean
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_23074
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras
Mosbahi, Bouzid
Basdouri, Imed
Lerbet, Jean
Rings and Algebras
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.
title Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras
topic Rings and Algebras
url https://arxiv.org/abs/2512.23074