The Lie algebra of homeomorphisms of the circle
type: Item
instance of: scholarly article
title: The Lie algebra of homeomorphisms of the circle
zbMATH Open document ID: 0935.17009
author: Robert Penner
author: Fyodor Malikov
published in: Advances in Mathematics
publication date: 1999-12-06T00:00:00Z
review text: The authors define and study an infinite-dimensional Lie algebra \(\text{homeo}_+\) directly related to the topological Lie group \(\text{Homeo}_+\) of all orientation preserving homeomorphisms of the circle. They use the second-named author's notion of universal decorated Teichmüller theory [Adv. Math. 98, No. 2, 143-215 (1993; Zbl 0772.30040)] to give Fréchet coordinates on \(\text{Homeo}_+\) modulo the group or real fractional linear transformations. The vector fields on the circle arising from this quotient group are then extended by the Lie algebra \(\text{sl}_2\), giving their \(\text{homeo}_+\). The approach is fundamentally arithmetic, the basic deformations being indexed by the modular group of integer fractional linear transformations.
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 1268552
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Lie algebras
zbMATH Keywords: Fréchet coordinates
reviewed by: Thomas A. Schmidt
MaRDI profile type: Publication
Wikidata QID: Q115396393
full work available at URL: aima.1998.1774
OpenAlex ID: W2068020863
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DOI: 10.1006/AIMA.1998.1774
description: scientific article; zbMATH DE number 1268552