Transposed BiHom-Poisson algebras

TL;DR

This paper introduces transposed BiHom-Poisson algebras, explores their properties, tensor product closure, and connections to TBP 3-Lie algebras, with examples of low-dimensional cases.

Contribution

It defines transposed BiHom-Poisson algebras and establishes their fundamental properties and relations to other algebraic structures.

Findings

Tensor product of TBP algebras is closed.

TBP algebras induce TBP 3-Lie algebras.

Examples of 2-dimensional TBP algebras are provided.

Abstract

In this paper, we introduce the concept of transposed BiHom-Poisson (abbr. TBP) algebras which can be constructed by the BiHom-Novikov-Poisson algebras. Several useful identities for TBP algebras are provided. We also prove that the tensor product of two (T)BP algebras are closed. The notions of BP 3-Lie algebras and TBP 3-Lie algebras are presented and TBP algebras can induce TBP 3-Lie algebras by two approaches. Finally, we give some examples for the TBP algebras of dimension 2.