Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T00:35:19.124Z Has data issue: false hasContentIssue false
  • English
  • Français

A family of crystallographic groups with 2-torsion in K0 of the rational group algebra

Published online by Cambridge University Press:  20 January 2009

P. H. Kropholler  and
B. Moselle
P. H. Kropholler
Affiliation:
School of Mathematical SciencesQueen Mary and Westfield CollegeMile End RoadLondon E1 4NS
B. Moselle
Affiliation:
School of Mathematical SciencesQueen Mary and Westfield CollegeMile End RoadLondon E1 4NS
Rights & Permissions [Opens in a new window]

Extract

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.

We calculate K0 of the rational group algebra of a certain crystallographic group, showing that it contains an element of order 2. We show that this element is the Euler class, and use our calculation to produce a whole family of groups with Euler class of order 2.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 325 - 331
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Brown, K. S., Complete Euler characteristics and fixed point theory, J. Pure Appl. Algebra 24 (1982), 103–121.CrossRefGoogle Scholar
2.Farrell, F. T., A remark on K 0 of crystallographic groups, Topology Appl. 26 (1987), 97–99.CrossRefGoogle Scholar
3.Lorenz, M., The rank of G0 for polycyclic group algebras, preprint.Google Scholar
4.Maclane, S., Categories for the working mathematician (Graduate Texts in Maths 5, Springer, New York, 1971).Google Scholar
5.Moody, J. A., Induction theorems for infinite groups, Bull. Amer. Math. Soc. (1) 17 (1987), 113–116.CrossRefGoogle Scholar
6.Quinn, F., Algebraic K-theory of poly-(fmite or cyclic) groups, Bull. Amer. Math. Soc. (1) 12 (1985), 221–226.CrossRefGoogle Scholar
7.Waldhausen, F., Whitehead groups of generalised free products, in Algebraic K-theory II (Lecture Notes in Mathematics 342, 1973, Springer, Berlin), 155–179.Google Scholar