Projective Dimension in Filtrated K-Theory
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Under mild assumptions, we characterise modules with projective resolutions of length n∈N in the target category of filtrated K-theory over a finite topological space in terms of two conditions involving certain Tor -groups. We show that the filtrated K-theory of any separable C∗dash-algebra over any topological space with at most four points has projective dimension 2 or less. We observe that this implies a universal coefficient theorem for rational equivariant KK-theory over these spaces. As a contrasting example, we find a separable C∗dash-algebra in the bootstrap class over a certain five-point space, the filtrated K-theory of which has projective dimension 3. Finally, as an application of our investigations, we exhibit Cuntz-Krieger algebras which have projective dimension 2 in filtrated K-theory over their respective primitive spectrum.
Original language | English |
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Title of host publication | Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012 |
Editors | Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov |
Publisher | Springer |
Publication date | 2013 |
Pages | 41-62 |
ISBN (Print) | 9783642394584 |
ISBN (Electronic) | 9783642394591 |
DOIs | |
Publication status | Published - 2013 |
Series | Springer Proceedings in Mathematics & Statistics |
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Volume | 58 |
ID: 95585533