Exact structures for operator modules

We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a decisive role in this.

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Bibliographic Details
Published in:Canadian journal of mathematics 2023-04, Vol.75 (2), p.421-446
Main Authors: Mathieu, Martin, Rosbotham, Michael
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Modules
Operators (mathematics)
Tensors
Terminology
Citations: Items that this one cites
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Description
Summary:We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a decisive role in this.
ISSN:0008-414X
1496-4279
DOI:10.4153/S0008414X22000037