On split regular BiHom-Poisson color algebras
BiHom-type algebra is a new topic, hence it is interesting to know in detail about its structure. In particular, the paper provides interesting results to the split regular BiHom-Poisson color algebras which are the natural extension of the one of split BiHom-Poisson algebras and so of split Hom-Poisson color algebras. As is well-known, the class of the split algebras is specially to addition quantum numbers, graded contractions, and deformations. Determining the structure of split BiHom-type algebras will become more and more meaningful in the area of research in mathematical physics. In the present paper, the authors first introduce the notion of a split regular BiHom-Poisson color ralgebra and study its structure. Furthermore, they show that a split regular BiHom-Poisson color algebra is the direct sum of its minimal ideals each one being a simple split regular BiHom-Poisson color algebra. To do that, the authors develop techniques of connections of roots in this framework. That is, an equivalence relation on the set of non-zero roots is given. Then it is shown that any equivalence class, associate to the quotient set induced by the equivalence relation, gives rise to an ideal. This family of ideals will be the one which forms the above announced decomposition. Finally, under suitable conditions, the simplicity of the split regular BiHom-Poisson color algebra is characterized. To get the characterization of the simplicity, the authors consider the subclass formed for those split regular BiHom-Poisson color algebras which are root-muiltiplicative and of maximal length.
scientific article; zbMATH DE number 7435670
scientific article