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• # Artykuł - szczegóły

## Colloquium Mathematicum

2016 | 145 | 1 | 1-13

## The structure of split regular Hom-Poisson algebras

EN

### Abstrakty

EN
We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra 𝔓 is of the form $𝔓 = U + ∑_{j} I_{j}$ with U a linear subspace of a maximal abelian subalgebra H and any $I_{j}$ a well described (split) ideal of 𝔓, satisfying ${I_{j},I_{k}} + I_{j}I_{k} = 0$ if j ≠ k. Under certain conditions, the simplicity of 𝔓 is characterized, and it is shown that 𝔓 is the direct sum of the family of its simple ideals.

1-13

wydano
2016

### Twórcy

• Department of Mathematics, Faculty od Sciences, University of Cádiz, 11510 Puerto Real, Cádiz, Spain
• Department of Mathematics, Faculty od Sciences, University of Cádiz, 11510 Puerto Real, Cádiz, Spain