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Groupoids as bridges between algebra and analysis

Grant


Scheme


  • Discovery Projects

Abstract


  • This project is in pure mathematics and focuses on the interplay between abstract algebra and the area of functional analysis known as operator algebras. Specifically, it deals with generalisations of graph C*-algebras and of Leavitt path algebras. Over the last decade, researchers have discovered striking similarities between these areas, but no unifying result that would allow them to transfer techniques and theorems systematically from one to the other. Recent research suggests that groupoid models for both algebras and C*-algebras may provide the missing link. This project will determine the role of groupoids in the two theories, and analyse and exploit the resulting synergies between abstract algebra and operator algebras.

Date/time Interval


  • 2015

Sponsor Award Id


  • DP150101598

Local Award Id


  • 116817

Scheme


  • Discovery Projects

Abstract


  • This project is in pure mathematics and focuses on the interplay between abstract algebra and the area of functional analysis known as operator algebras. Specifically, it deals with generalisations of graph C*-algebras and of Leavitt path algebras. Over the last decade, researchers have discovered striking similarities between these areas, but no unifying result that would allow them to transfer techniques and theorems systematically from one to the other. Recent research suggests that groupoid models for both algebras and C*-algebras may provide the missing link. This project will determine the role of groupoids in the two theories, and analyse and exploit the resulting synergies between abstract algebra and operator algebras.

Date/time Interval


  • 2015

Sponsor Award Id


  • DP150101598

Local Award Id


  • 116817