Tensor $D$ coaction functors
S. Kaliszewski, Magnus B. Landstad, John Quigg
TL;DR
This paper introduces tensor D coaction functors, proving their exactness and identifying the minimal such functor, advancing tools to address the Baum-Connes conjecture in operator algebras.
Contribution
It develops tensor D coaction functors, proving their exactness and identifying the minimal functor, enhancing the toolkit for Baum-Connes conjecture research.
Findings
Tensor D coaction functors are exact.
The minimal tensor D coaction functor is identified.
Supports the Baum-Connes conjecture program.
Abstract
We develop an approach, using what we call "tensor coaction functors", to the "-crossed-product" functors of Baum, Guentner, and Willett. We prove that the tensor functors are exact, and identify the minimal such functor. This continues our program of applying coaction functors as a tool in the Baum-Guentner-Willett-Buss-Echterhoff campaign to attempt to "fix" the Baum-Connes conjecture.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology