The generalized Heisenberg group arising from Weyl relations

In this paper, we introduce the generalized Weyl operators canonically associated with the one-mode oscillator Lie algebra as unitary operators acting on the bosonic Fock space Γ (C). Next, we establish the generalized Weyl relations and deduce a group structure on the manifold R2× [- π, π[× R generalizing the well-known Heisenberg one in a natural way. © 2015, Chapman University.