On the isomorphism between the reduction algebra and the invariant differential operators on Lie groups

TL;DR

This paper demonstrates a non-canonical isomorphism between the reduction algebra and invariant differential operators on Lie groups using deformation quantization, with additional results on algebra deformations.

Contribution

It establishes a novel algebra isomorphism via deformation quantization techniques, linking reduction algebras and invariant differential operators on Lie groups.

Findings

Non-canonical algebra isomorphism established

Results on deformations of the involved algebras

Application of deformation quantization methods

Abstract

Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these two algebras are also proved. Part of the author's PhD thesis at University Paris 7, 2009.