Towards a sheaf cohomology theory for C*-algebras

Martin Mathieu

Towards a sheaf cohomology theory for C*-algebras

Martin Mathieu

School of Mathematics and Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

In joint work with Pere Ara (Barcelona) we are in the process of developing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operator module sheaves over sheaves of C*-algebras are non-abelian and therefore the homology theory needed has to be set in the more general framework
of exact categories.

Original language	English
Title of host publication	Banach Algebras and Applications 2017, Oulu, Finland
Publisher	Walter de Gruyter & Co., Germany
Pages	1-17
ISBN (Electronic)	978-3-11-021809-1
ISBN (Print)	978-3-11-021808-4
Publication status	Accepted - 01 Feb 2019

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Towards a sheaf cohomology theory for C*-algebras
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AB - In joint work with Pere Ara (Barcelona) we are in the process of developing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operator module sheaves over sheaves of C*-algebras are non-abelian and therefore the homology theory needed has to be set in the more general frameworkof exact categories.

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BT - Banach Algebras and Applications 2017, Oulu, Finland

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