On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures

TL;DR

This paper investigates the Lie algebra structure of generators of infinitesimal symmetries in almost-cosymplectic-contact structures on odd-dimensional manifolds, revealing subalgebra structures related to tensor fields.

Contribution

It characterizes Lie subalgebras of symmetry generators associated with almost-cosymplectic-contact structures, providing new insights into their algebraic properties.

Findings

Lie algebra structure on pairs of 1-forms and functions

Description of subalgebras generated by symmetries of tensor fields

Enhanced understanding of symmetry generators in geometric structures

Abstract

We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.