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On the graded Lie algebra of quantisable forms

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*Josef Janyška and Marco Modugno*

**E-mail:** janyska@math.muni.cz, modugno@dma.unifi.it
**Abstract.** A quantisable form is defined to be a form on the 1-jet
space of spacetime whose Hamiltonian lift is a tangent valued form projectable
on spacetime. The quantisable forms constitute a graded Lie algebra with
respect to a natural bracket. A natural homomorphism from the algebra of
quantisable forms to the Fr\"olicher--Nijenhuis algebra of tangent valued
forms on the spacetime is exhibited.

**AMSclassification.** 53C05, 58A20, 70H40, 81S10, 83C10

**Keywords.** Galilei spacetime, phase space, jets, connections,
Hamiltonian lift, quantisable form