ABSTRACT

We consider algebraic systems with several products, including unary products, $\mathfrak{S}$ (as examples we can take linear spaces, algebras, superalgebras, hom-algebras, triple systems, hom-triple systems, Poisson algebras, Bol algebras, n-algebras, etc.) We show that any basis of $\mathfrak{S}$ gives rise to a decomposition of $\mathfrak{S}$ as a direct sum of indecomposable well-described ideals (fine decomposition). The simplicity of the components in this decomposition is also characterized. There are as many non-isomorphic fine decompositions as orbits in a determined action.

中文翻译：

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由基诱导的代数系统的精细分解

摘要

我们考虑具有多个产品的代数系统，包括一元产品，$\mathfrak{小号}$（例如，我们可以采用线性空间、代数、超代数、hom-代数、三重系统、hom-三重系统、泊松代数、Bol 代数、n-代数等。）我们证明了$\mathfrak{小号}$导致分解$\mathfrak{小号}$作为不可分解的良好描述理想的直接总和（精细分解）。此分解中组件的简单性也具有特征。在确定的动作中，有与轨道一样多的非同构精细分解。