2023/03/24 by Valiollah Khalili, Khalili, Valiollah
Mathematics · #17A60 #17B05 #17B63 #17B75 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #G.0 #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2303.13832
openalex publication_date 2023/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the class of graded Poisson color algebras as the natural generalization of graded Poisson algebras and graded Poisson superalgebras. For Λ an arbitrary abelian group, we show that any of such Λ-graed Poisson color algebra P, with a symmetric Λ-support is of the form P = U⊕∑j Ij, with U a subspace of P1 and any Ij a well described graded ideal of P, satisfying \Ij, Ik\+Ij Ik=0 if j≠ i. Furthermore, under certain conditions, the gr-simplicity of P is characterized and it is shown that P is the direct sum of the family of its graded simple ideals.