Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-16T09:58:52.433Z Has data issue: false hasContentIssue false
  • English
  • Français

K-groups of rings and the homology of their elementary matrix groups

Part of: Categories and geometry Homological algebra

Published online by Cambridge University Press:  09 April 2009

Janet Aisbett
Janet Aisbett
Affiliation:
Department of Mathematics University of QueenslandSt. Lucia 4067 Queensland, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Low dimensional algebraic K-groups of a commutative ring are described in terms of the homology of its elementary matrix group. This approach is prompted by recent successful computations of low-dimensional K-groups using group homology methods, and it builds on the identity K2(R)=H2(ER).

MSC classification

Secondary: 18F25: Algebraic $K$-theory and $L$-theory 18G40: Spectral sequences, hypercohomology
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 268 - 274
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Aisbett, J., Lluis-Puebla, E., Snaith, V. and Soulé, C., ‘On K*(Z/n) and K*(Fq[t]/(t2))’, Memoirs Amer. Math. Soc., to appear.Google Scholar
[2]Dennis, K. and Stein, M., ‘K2 of discrete valuation rings,’ Adv. in Math. 18 (1975), 182–238.CrossRefGoogle Scholar
[3]Evens, L. and Friedlander, E., ‘On K*(Z/p2 Z) and related homology groups’ Trans. Amer. Math. Soc. 270 (1982), 1–46.Google Scholar
[4]Eilenberg, S. and Lane, S. Mac, ‘On the groups H(Π, n)’ II, Annals of Math. 60 (1954), 49–139.CrossRefGoogle Scholar
[5]Loday, J. -L., ‘K-théorie algébrique et représentations de groupes,’ Ann. Sci.École Norm. Sup., (4) 9 (1976), 309–377.CrossRefGoogle Scholar
[6]Lee, R. and Szczarba, R., ‘The group K3(Z) is cyclic of order 48, Ann. of Math. 104 (1976), 31–60.CrossRefGoogle Scholar
[7]Soulé, C., ‘Cohomology of SL3Z,’ Topology 17 (1978), 1–22.CrossRefGoogle Scholar
[8]Wagoner, J., ‘Delooping classifying spaces in algebraic K-theory,’ Topology 11 (1972), 349–370.CrossRefGoogle Scholar
[9]Whitehead, J., ‘A certain exact sequence’ Ann. of Math. 2 (1950), 51–95.CrossRefGoogle Scholar