Projective Dimension in Filtrated K-Theory

Rasmus Moritz Bentmann

doi:10.1007/978-3-642-39459-1_3

Projective Dimension in Filtrated K-Theory

Rasmus Moritz Bentmann

Institut for Matematiske Fag

1 Citationer (Scopus)

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.

Originalsprog	Engelsk
Titel	Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012
Redaktører	Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov
Forlag	Springer
Publikationsdato	2013
Sider	41-62
ISBN (Trykt)	9783642394584
ISBN (Elektronisk)	9783642394591
DOI	https://doi.org/10.1007/978-3-642-39459-1_3
Status	Udgivet - 2013

Navn	Springer Proceedings in Mathematics & Statistics
Vol/bind	58

Adgang til dokumentet

10.1007/978-3-642-39459-1_3

http://link.springer.com/book/10.1007%2F978-3-642-39459-1

Citationsformater

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 › peer review

@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",

}

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 -

Projective Dimension in Filtrated K-Theory

Abstract

Adgang til dokumentet

Fingeraftryk

Citationsformater