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

## Josef Janyška

Address: Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: janyska@math.muni.cz

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.

AMSclassification: primary 53C15.

Keywords: almost-cosymplectic-contact structure, almost-coPoisson-Jacobi structure, infinitesimal symmetry, Lie algebra.

DOI: 10.5817/AM2016-5-325