2023/04/12 by Valiollah Khalili, Khalili, Valiollah
Mathematics · #17A30 #17A60 #17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #G.0 #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2304.05745
openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study of the structure of non-commutative Poisson algebras with an arbitrary set ß. We show that any of such an algebra \pp decomposes as \pp=\uu⊕∑_[λ]∈(Λ_ß∖\0\)/∼\pp[λ], where \uu is a linear subspace complement of \span\bbbf\ [\ppμ, \ppη]+\ppμ\ppη : μ, η∈[\lam]\∩\pp0 in \pp0 and any \pp[λ] a well-described graded ideals of \pp, satisfying [\pp[λ], \pp[μ]]+\pp[λ] \pp[μ]=0 if [λ]≠[μ]. Under certain conditions, the simplicity of \pp is characterized and it is shown that \pp is the direct sum of the family of its graded simple ideals.