Topic
Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a non-commutative Yang-Mills theory with D-brane backgrounds in IIB matrix model was proposed. But it is not a generalization of noncommutativity.
370 citations
TL;DR: In this article, the quantum deformations of cluster algebras are studied in the context of total positivity and canonical bases in semisimple groups and their quantum analogs.
363 citations
01 Jan 1996
TL;DR: In this article, the authors present an investigation of the massless, two-dimentional, interacting field theories and their invariance under an infinite-dimensional group of conformal transformations.
Abstract: We present an investigation of the massless, two-dimentional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of Virasoro algebra, and that the correlation functions are built up of the “conformal blocks” which are completely determined by the conformal invariance. Exactly solvable conformal theories associated with the degenerate representations are analyzed. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy the systems of linear differential equations.
357 citations
352 citations
TL;DR: In this paper, the massless quantum field theories describing the critical points in two-dimensional statistical systems were studied and it was shown that the local fields forming the operator algebra can be classified according to irreducible representations of the Virasoro algebra.
Abstract: We study the massless quantum field theories describing the critical points in two dimensional statistical systems. These theories are invariant with respect to the infinite dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the Virasoro algebra. Exactly solvable theories associated with degenerate representations are analized. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations.
350 citations