Convergent star products on cotangent bundles of Lie groups

Abstract For a connected real Lie group G we consider the canonical standard-ordered star product arising from global symbol calculus based on half-commutator connection of . This trivially converges polynomial functions $$T^*G$$ T ∗ G thanks to its homogeneity. We define nuclear Fréchet algebra certain analytic , for which is shown be well-defined continuous multiplication, depending holomorphically deformation parameter $$\hbar $$ ħ realized as completed (projective) tensor entire with an appropriate $${\mathfrak {g}}^*$$ g The passage Weyl-ordered product, i.e. Gutt preserve this function space, yielding continuity holomorphic dependence