Gauge symmetry of unimodular gravity in Hamiltonian formalism

We work out the description of gauge symmetry unimodular gravity in constrained Hamiltonian formalism. In particular, we demonstrate how transversality conditions restricting diffeomorphism parameters emerge from algebra constraints. The alternative form is long known as parametrizing volume preserving diffeomorphisms by unrestricted two-forms instead transverse vector fields. This reducible. this (UG) symmetry. Becchi-Rouet-Stora-Tyutin--Batalin-Fradkin-Vilkovisky (BFV-BRST) formalism constructed for both forms UG These two BRST complexes have a subtle inequivalence: Their cohomology groups are not isomorphic. first complex, which related to restricted parameters, cosmological constant does correspond any nontrivial cocycle, while complex it does. wording physics, means $\mathrm{\ensuremath{\Lambda}}$ fixed parameter defined field asymptotics rather than physical observable standpoint complex. second views with initial data.