2026/2/8
Valiollah Khalili

Valiollah Khalili

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0001-9571-7394
Education: PhD.
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Faculty: Science
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E-mail: v-khalili [at] araku.ac.ir
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Research

Title
ON THE STRUCTURE OF GRADED POISSON COLOR ALGEBRAS
Type
JournalPaper
Keywords
Poisson color algebras, graded algebras and structure theory.
Year
2025
Journal Communications of the Korean Mathematical Society
DOI
Researchers Valiollah Khalili

Abstract

In this paper we introduce a class of graded Poisson color algebras as a natural generalization of graded Poisson algebras and graded Poisson superalgebras. For Λ an arbitrary abelian group, we show that any of such Λ-graded Poisson color algebra P, with a symmetric Λ-support is of the form P = U ⊕ P 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.