The structure of split regular Hom-Poisson algebras

• Autorzy: María J. Aragón Periñán , Antonio J. Calderón Martín
• Języki publikacji: 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.

Kategorie tematyczne

• 17A60: Structure theory
• 17B22: Root systems
• 17A30: Algebras satisfying other identities
• 17B63: Poisson algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 145
• Numer: 1
• Strony: 1-13

Daty

wydano

2016

Twórcy

autor

María J. Aragón Periñán

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

autor

Antonio J. Calderón Martín

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

Identyfikatory

DOI

10.4064/cm6568-9-2015