Tbilisi Mathematical Journal
- Tbilisi Math. J.
- Volume 1 (2008), 165-210.
Homological algebra in bivariant K-theory and other triangulated categories. II
We use homological ideals in triangulated categories to get a sufficient criterion for a pair of subcategories in a triangulated category to be complementary. We apply this criterion to construct the Baum-Connes assembly map for locally compact groups and torsion-free discrete quantum groups. Our methods are related to the abstract version of the Adams spectral sequence by Brinkmann and Christensen.
Supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.
Tbilisi Math. J., Volume 1 (2008), 165-210.
Received: 17 July 2008
Revised: 4 December 2008
Accepted: 15 December 2008
First available in Project Euclid: 12 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18E30: Derived categories, triangulated categories
Secondary: 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 55U35: Abstract and axiomatic homotopy theory
Meyer, Ralf. Homological algebra in bivariant K-theory and other triangulated categories. II. Tbilisi Math. J. 1 (2008), 165--210. doi:10.32513/tbilisi/1528768828. https://projecteuclid.org/euclid.tbilisi/1528768828