Classification of infinitesimal symmetries in covariant classical mechanics

In the framework of general relativistic classical mechanics on a spacetime with absolute time, we classify the infinitesimal symmetries of the classical structure by means of distinguished Lie subalgebras of the Lie algebra of "special phase functions". These subalgebras are crucial also for the classification of infinitesimal quantum symmetries, which will be analysed in a forthcoming paper. Key words: covariant classical mechanics, Lie algebras and symmetries, jets, cosymplectic manifolds. 2000 MSC: 17B26, 17B81, 37J05, 37J15, 58A20, 55R05, 55R10, 70H33, 83C99.