Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.10370 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918302929911808 |
|---|---|
| author | Chen, Yin Zhang, Runxuan |
| author_facet | Chen, Yin Zhang, Runxuan |
| contents | We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence classes and extendability of deformations for a fixed left-symmetric color algebra, demonstrating that each infinitesimal deformation is nontrivially extendable if the third cohomology subspace of degree zero is trivial. We also study Nijenhuis operators and Rota-Baxter operators on a left-symmetric color algebra, providing a better understanding of the equivalence class of the trivial infinitesimal deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of left-symmetric color algebras Chen, Yin Zhang, Runxuan Rings and Algebras 17D25, 17B75 We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence classes and extendability of deformations for a fixed left-symmetric color algebra, demonstrating that each infinitesimal deformation is nontrivially extendable if the third cohomology subspace of degree zero is trivial. We also study Nijenhuis operators and Rota-Baxter operators on a left-symmetric color algebra, providing a better understanding of the equivalence class of the trivial infinitesimal deformation. |
| title | Deformations of left-symmetric color algebras |
| topic | Rings and Algebras 17D25, 17B75 |
| url | https://arxiv.org/abs/2411.10370 |