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Equilibrium states and fine structure for operator algebras

Grant


Scheme

  • Discovery Projects

Abstract

  • This project is in pure mathematics, in the broad area of functional analysis, and focuses specifically on operator algebras. Kubo-Martin-Schwinger (KMS) states on operator algebras encode equilibria of C*-algebraic dynamical systems. This project takes a novel view of KMS data as a repository of fine operator-algebraic structure. It will develop a theory whereby KMS states recover structural details like primitive-ideal structure and simplicity. The project will determine to what extent the KMS simplex of a combinatorial operator algebra remembers underlying combinatorial data. It will also explore KMS states on combinatorial operator algebras as a new point of interaction between the two main branches of modern operator-algebra theory.

Sponsor Award Id

  • DP150101595

Local Award Id

  • 116243

Scheme

  • Discovery Projects

Abstract

  • This project is in pure mathematics, in the broad area of functional analysis, and focuses specifically on operator algebras. Kubo-Martin-Schwinger (KMS) states on operator algebras encode equilibria of C*-algebraic dynamical systems. This project takes a novel view of KMS data as a repository of fine operator-algebraic structure. It will develop a theory whereby KMS states recover structural details like primitive-ideal structure and simplicity. The project will determine to what extent the KMS simplex of a combinatorial operator algebra remembers underlying combinatorial data. It will also explore KMS states on combinatorial operator algebras as a new point of interaction between the two main branches of modern operator-algebra theory.

Sponsor Award Id

  • DP150101595

Local Award Id

  • 116243