Projective Dimension in Filtrated K-Theory
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Projective Dimension in Filtrated K-Theory. / Bentmann, Rasmus Moritz.
Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. red. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. s. 41-62 (Springer Proceedings in Mathematics & Statistics , Bind 58).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Projective Dimension in Filtrated K-Theory
AU - Bentmann, Rasmus Moritz
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-642-39459-1_3
DO - 10.1007/978-3-642-39459-1_3
M3 - Article in proceedings
SN - 9783642394584
T3 - Springer Proceedings in Mathematics & Statistics
SP - 41
EP - 62
BT - Operator Algebra and Dynamics
A2 - Clausen, Toke M.
A2 - Eilers, Søren
A2 - Restorff, Gunnar
A2 - Silvestrov, Sergei
PB - Springer
ER -
ID: 95585533