Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra
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_ | 1866909547298291712 |
|---|---|
| author | Abramov, Viktor Sovetnikov, Nikolai |
| author_facet | Abramov, Viktor Sovetnikov, Nikolai |
| contents | One important example of a transposed Poisson algebra can be constructed by means of a commutative algebra and its derivation. This approach can be extended to superalgebras, that is, one can construct a transposed Poisson superalgebra given a commutative superalgebra and its even derivation. In this paper we show that including odd derivations in the framework of this approach requires introducing a new notion. It is a super vector space with two operations that satisfy the compatibility condition of transposed Poisson superalgebra. The first operation is determined by a left supermodule over commutative superalgebra and the second is a Jordan bracket. Then it is proved that the super vector space generated by an odd derivation of a commutative superalgebra satisfies all the requirements of introduced notion. We also show how to construct a 3-Lie superalgebra if we are given a transposed Poisson superalgebra and its even derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra Abramov, Viktor Sovetnikov, Nikolai Mathematical Physics Commutative Algebra 17B63 One important example of a transposed Poisson algebra can be constructed by means of a commutative algebra and its derivation. This approach can be extended to superalgebras, that is, one can construct a transposed Poisson superalgebra given a commutative superalgebra and its even derivation. In this paper we show that including odd derivations in the framework of this approach requires introducing a new notion. It is a super vector space with two operations that satisfy the compatibility condition of transposed Poisson superalgebra. The first operation is determined by a left supermodule over commutative superalgebra and the second is a Jordan bracket. Then it is proved that the super vector space generated by an odd derivation of a commutative superalgebra satisfies all the requirements of introduced notion. We also show how to construct a 3-Lie superalgebra if we are given a transposed Poisson superalgebra and its even derivation. |
| title | Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra |
| topic | Mathematical Physics Commutative Algebra 17B63 |
| url | https://arxiv.org/abs/2503.16900 |