# Janyška J. On the Lie algebra of generators of infinitesimal symmetries almost-cosymplectic-contact structures, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

An almost-cosymplectic-contact (ACC) structure (pair) on an odd dimensional manifold ${\displaystyle \mathbf {M} }$ is given by a pair ${\displaystyle (\omega ,\Omega )}$ of a 1-form and a 2-form such that
${\displaystyle d\Omega =0\,,\quad \omega \wedge \Omega ^{n}\not \equiv 0\,.}$
As an infinitesimal symmetry of the ACC structure we assume a vector field ${\displaystyle X}$ on ${\displaystyle \mathbf {M} }$ such that ${\displaystyle L_{X}\omega =0}$ and ${\displaystyle L_{X}\Omega =0}$.
Infinitesimal symmetries are generated by pairs of functions ${\displaystyle (f,h)}$ on ${\displaystyle \mathbf {M} }$. We show that generators of infinitesimal symmetries of ${\displaystyle (\omega ,\Omega )}$ form a Lie algebra. As an example we describe the Lie algebra of infinitesimal symmetries of the ACC structure of the phase space of the classical spacetime given as the 1-jet space of motions.