Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics
type: Item
instance of: scholarly article
title: Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics
zbMATH Open document ID: 0671.46033
DOI: 10.1007/BF01217736
author: David E. Evans
author: Alain Connes
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The authors construct and analyse actions of GL(\(\infty)\) on the operator algebras of V. Jones and A. Ocneanu. They characterize algebraically - using generators and relations - representations of the Lie algebra gl(\(\infty)\) where the images of the elementary matrices \(E_{ii}\) are represented by projections. They then show that these relations can be realized in the AF-algebras of V. Jones and A. Ocneanu.
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 4098060
zbMATH Keywords: actions of GL(\(\infty )\)
zbMATH Keywords: Lie algebra
zbMATH Keywords: AF-algebras
reviewed by: Joachim Cuntz
MaRDI profile type: Publication
cites work: Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
cites work: Analyticity of correlation functions for the two-dimensional Ising model
cites work: On a \(C^*\)-algebra approach to phase transition in the two-dimensional Ising model
cites work: Q3324796
cites work: Infinite conformal symmetry in two-dimensional quantum field theory
cites work: Q3913911
cites work: Q3032826
cites work: Non-commutative differential geometry
cites work: Caractère multiplicatif d'un module de Fredholm. (Multiplicative character of a Fredholm module)
cites work: On fermionic gauge groups, current algebras and Kac-Moody algebras
cites work: On a \(C^ *\)-algebra approach to phase transition in the two-dimensional Ising model. II
cites work: Unitary representations of the Virasoro and super-Virasoro algebras
cites work: Index for subfactors
cites work: Q3761115
cites work: Q3472677
cites work: Two-dimensional Ising correlations: Convergence of the scaling limit
cites work: Two-dimensional Ising correlations: The SMJ analysis
cites work: A groupoid approach to C*-algebras
cites work: Holonomic quantum fields. V
cites work: Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
full work available at URL: https://doi.org/10.1007/bf01217736
OpenAlex ID: W2096005655
description: scientific article; zbMATH DE number 4098060