Kupershmidt-Nijenhuis structures on pre-Malcev algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915671198138368 |
|---|---|
| author | Chen, Yin Qin, Liman Ren, Shan Zhang, Runxuan |
| author_facet | Chen, Yin Qin, Liman Ren, Shan Zhang, Runxuan |
| contents | We study Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on finite-dimensional pre-Malcev algebras over a field of characteristic zero. We construct several new families of complex pre-Malcev algebras that are not pre-Lie algebras in dimensions two, three and four. We use the compatibility of linear operators to establish connections between Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on pre-Malcev algebras. Moreover, we use a method from computational ideal theory to characterize the geometric structures of the varieties of Kupershmidt operators and Nijenhuis operators on a three-dimensional complex pre-Malcev algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11841 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Kupershmidt-Nijenhuis structures on pre-Malcev algebras Chen, Yin Qin, Liman Ren, Shan Zhang, Runxuan Rings and Algebras 17A30, 17D10, 17A60, 13P25 We study Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on finite-dimensional pre-Malcev algebras over a field of characteristic zero. We construct several new families of complex pre-Malcev algebras that are not pre-Lie algebras in dimensions two, three and four. We use the compatibility of linear operators to establish connections between Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on pre-Malcev algebras. Moreover, we use a method from computational ideal theory to characterize the geometric structures of the varieties of Kupershmidt operators and Nijenhuis operators on a three-dimensional complex pre-Malcev algebra. |
| title | Kupershmidt-Nijenhuis structures on pre-Malcev algebras |
| topic | Rings and Algebras 17A30, 17D10, 17A60, 13P25 |
| url | https://arxiv.org/abs/2208.11841 |