In this short note we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.

The affine coherent states quantization is a promising integral of Hamiltonian systems when the phase space includes at least one conjugate pair variables which takes values from half plane. Such situation common for gravitational include singularities. construction map one-to-one mapping plane onto group. Particular cases this define specific parametrizations Our aim showing that different suc...