Kupershmidt operators on 3-BiHom-Poisson color algebras and 3-BiHom-pre-Poisson color algebra structures
摘要
The purpose of this paper is to introduce the class of 3-BiHom-Poisson color algebras, which is a combination of 3-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of 3-BiHom-pre-Poisson color algebras and investigate the relationship between 3-BiHom-Poisson color algebras and 3-BiHom-pre-Poisson color algebras via Kupershmidt operators.