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)

Speaker: Josef Janyška

Title: On the Lie algebra of generators of infinitesimal symmetries almost-cosymplectic-contact structures

Abstract:
An almost-cosymplectic-contact (ACC) structure (pair) on an odd dimensional manifold $𝐌$ is given by a pair $(\omega ,\Omega )$ of a 1-form and a 2-form such that

$d\Omega =0,\omega \wedge {\Omega }^n\equiv ̸0.$

As an infinitesimal symmetry of the ACC structure we assume a vector field $X$ on $𝐌$ such that $L_X\omega =0$ and $L_X\Omega =0$.

Infinitesimal symmetries are generated by pairs of functions $(f,h)$ on $𝐌$. We show that generators of infinitesimal symmetries of $(\omega ,\Omega )$ 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.