Transposed BiHom-Poisson algebras. (English) Zbl 1533.17026
The paper under review introduces and studies the novel concept of transposed BiHom-Poisson algebras, abbreviated as TBP algebras, which can be constructed from BiHom-Novikov-Poisson algebras. The provided exploration includes valuable insights with several useful identities for TBP algebras. Notably, the study establishes the closure of the tensor product for two TBP algebras. The presentation further delves into the notions of BP 3-Lie algebras and TBP 3-Lie algebras, highlighting that TBP algebras can induce TBP 3-Lie algebras through two distinct approaches. The paper concludes by offering illustrative examples of 2-dimensional TBP algebras. Overall, the work contributes significant advancements in the understanding and application of transposed BiHom-Poisson algebras, providing a foundation for further exploration in this area.
Reviewer: Yin Chen (Changchun)
MSC:
| 17B61 | Hom-Lie and related algebras |
| 17D30 | (non-Lie) Hom algebras and topics |
| 17A30 | Nonassociative algebras satisfying other identities |
| 17B63 | Poisson algebras |
Keywords:
BiHom-Novikov-Poisson algebras; transposed BiHom-Poisson algebras; transposed BiHom-Poisson 3-Lie algebrasReferences:
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