The Poisson geometry of SU(1,1)

TL;DR

This paper explores the Poisson structure on SU(1,1), providing explicit descriptions of key isomorphisms and establishing an analogue of Thompson's conjecture for the group.

Contribution

It offers a detailed analysis of the Poisson geometry of SU(1,1), including explicit isomorphisms and a new analogue of Thompson's conjecture.

Findings

Explicit description of the Ginzburg-Weinstein isomorphism for SU(1,1)

Establishment of an analogue of Thompson's conjecture for SU(1,1)

Advancement in understanding the Poisson structure on non-compact Lie groups

Abstract

We study the natural Poisson structure on the Lie group SU(1,1) and related questions. In particular, we give an explicit description of the Ginzburg-Weinstein isomorphism for the sets of admissible elements. We also establish an analogue of Thompson's conjecture for this group.