\(\text{Diff }S^ 1\) as coadjoint orbit in the Virasoro space of moments
type: Item
instance of: scholarly article
title: \(\text{Diff }S^ 1\) as coadjoint orbit in the Virasoro space of moments
zbMATH Open document ID: 0801.58008
DOI: 10.1016/0393-0440(94)90037-X
author: Paul Donato
published in: Journal of Geometry and Physics
publication date: 1994-12-04T00:00:00Z
review text: A distribution \(T\) on \(S^ 1\) is defined by \(T(f)= \sum_{n\in\mathbb{N}} {f(n)\over 2^ n}\), where \(f\) is \(2\pi\)-periodic and differentiable. For any vector field \(\xi= f(\theta) {\partial\over \partial\theta}\) on \(S^ 1\), one has \[ \langle T\otimes d\theta\mid \xi\rangle= \sum_{n\in \mathbb{N}} {f(n)\over 2^ n}. \] The author proves that the isotropy subgroup of \(T\otimes d\theta\) for the coadjoint action of \(\text{Diff}(S^ 1)\) is reduced to the identity. So, he obtains an embedding of \(\text{Diff}(S^ 1)\) as a symplectic coadjoint orbit of itself. Also, an embedding of \(\text{Diff}(S^ 1)\) in the Virasoro group with non-zero central charge is presented.
reviewed by: Ion Mihai
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 569292
zbMATH Keywords: groups of diffeomorphisms
zbMATH Keywords: symplectic structures
zbMATH Keywords: Virasoro space of moments
MaRDI profile type: Publication
cites work: Q3963261
cites work: Q3724586
cites work: Unitary representations of some infinite dimensional groups
cites work: Coadjoint orbits of the Virasoro group
description: scientific article; zbMATH DE number 569292