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arXiv · 2303.13832

On the structure of graded Poisson color algebras

Valiollah Khalili
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Abstract

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 $\Lambda$ an arbitrary abelian group, we show that any of such $\Lambda$-graed Poisson color algebra $\mathcal{P}$, with a symmetric $\Lambda$-support is of the form $\mathcal{P} = \mathcal{U}\oplus\sum_j I_j$, with $\mathcal{U}$ a subspace of $\mathcal{P}_1$ and any $I_j$ a well described graded ideal of $\mathcal{P},$ satisfying $\{I_j, I_k\}+I_j I_k=0$ if $j\neq i.$ Furthermore, under certain conditions, the gr-simplicity of $\mathcal{P}$ is characterized and it is shown that $\mathcal{P}$ is the direct sum of the family of its graded simple ideals.

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Valiollah Khalili. 2023-03-24. On the structure of graded Poisson color algebras. https://arxiv.org/abs/2303.13832

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