Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics
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.
scientific article; zbMATH DE number 4098060
scientific article