Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918265204244480 |
|---|---|
| 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 |