Projective Dimension in Filtrated K-Theory

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Standard

Projective Dimension in Filtrated K-Theory. / Bentmann, Rasmus Moritz.

Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. ed. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. p. 41-62 (Springer Proceedings in Mathematics & Statistics , Vol. 58).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Harvard

Bentmann, RM 2013, Projective Dimension in Filtrated K-Theory. in TM Clausen, S Eilers, G Restorff & S Silvestrov (eds), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. Springer, Springer Proceedings in Mathematics & Statistics , vol. 58, pp. 41-62. https://doi.org/10.1007/978-3-642-39459-1_3

APA

Bentmann, R. M. (2013). Projective Dimension in Filtrated K-Theory. In T. M. Clausen, S. Eilers, G. Restorff, & S. Silvestrov (Eds.), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012 (pp. 41-62). Springer. Springer Proceedings in Mathematics & Statistics Vol. 58 https://doi.org/10.1007/978-3-642-39459-1_3

Vancouver

Bentmann RM. Projective Dimension in Filtrated K-Theory. In Clausen TM, Eilers S, Restorff G, Silvestrov S, editors, Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. Springer. 2013. p. 41-62. (Springer Proceedings in Mathematics & Statistics , Vol. 58). https://doi.org/10.1007/978-3-642-39459-1_3

Author

Bentmann, Rasmus Moritz. / Projective Dimension in Filtrated K-Theory. Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. editor / Toke M. Clausen ; Søren Eilers ; Gunnar Restorff ; Sergei Silvestrov. Springer, 2013. pp. 41-62 (Springer Proceedings in Mathematics & Statistics , Vol. 58).

Bibtex

@inproceedings{ea5ae1ab46564ecbb63b60bd896ba48e,
title = "Projective Dimension in Filtrated K-Theory",
abstract = "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.",
author = "Bentmann, {Rasmus Moritz}",
year = "2013",
doi = "10.1007/978-3-642-39459-1_3",
language = "English",
isbn = "9783642394584",
series = "Springer Proceedings in Mathematics & Statistics ",
pages = "41--62",
editor = "Clausen, {Toke M.} and Eilers, {S{\o}ren } and Restorff, {Gunnar } and Silvestrov, {Sergei }",
booktitle = "Operator Algebra and Dynamics",
publisher = "Springer",
address = "Switzerland",

}

RIS

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