Poisson Algebras of Admissible Functions Associated to Twisted Dirac Structures

TL;DR

This paper introduces Poisson algebras derived from admissible functions linked to twisted Dirac structures, expanding the understanding of their algebraic properties and specific cases involving non-degenerate 2-forms.

Contribution

It defines a new class of Poisson algebras associated with twisted Dirac structures and analyzes their properties in standard cases.

Findings

Admissible functions form Poisson algebras in the context of twisted Dirac structures

Standard cases related to graphs of non-degenerate 2-forms are studied

The structure of these Poisson algebras is characterized and understood

Abstract

We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.