Journal article
Smooth Lie group actions on non-commutative tori
Nonlinearity, Vol.2(2), pp.271-286
05/01/1989
DOI: 10.1088/0951-7715/2/2/004
Abstract
The irrational rotation algebras are the most studied and most accessible examples of 'non-commutative manifolds'. We investigate and classify smooth transformation groups on these algebras, using Lie algebraic techniques. The decisive question is the existence of representations of the Heisenberg Lie algebra by smooth 'vector fields'. We answer this, making use of the solution by Connes and Rieffel of the Yang-Mills problem for smooth 'vector bundles' over these algebras.
Details
- Title: Subtitle
- Smooth Lie group actions on non-commutative tori
- Creators
- Ola Bratteli - Univ Trondheim, Inst Math, N-7034 Trondheim, NorwayGeorge A Elliott - Univ Copenhagen, Math Inst, DK-2100 Copenhagen, DenmarkF. M Goodman - Univ Iowa, Dept Math, Iowa City, IA 52242 USAPalle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Nonlinearity, Vol.2(2), pp.271-286
- Publisher
- IOP PUBLISHING LTD
- DOI
- 10.1088/0951-7715/2/2/004
- ISSN
- 0951-7715
- eISSN
- 1361-6544
- Number of pages
- 16
- Grant note
- NSF, USA; National Science Foundation (NSF) NSERC of Canada; Natural Sciences and Engineering Research Council of Canada (NSERC)
- Language
- English
- Date published
- 05/01/1989
- Academic Unit
- Mathematics
- Record Identifier
- 9984241055502771
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