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Hecke Algebras and Class-Group Invariants

Published online by Cambridge University Press:  20 November 2018

V. P. Snaith
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Abstract

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Let G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ψ, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising fromthe Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ψ. As an application we show that two such constructions coincide.

Keywords

16S3419A9911R65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1265 - 1280
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Chinburg, T., Kolster, M., Pappas, G. and Snaith, V.P., Galois structure of K-groups of rings of integers. C.R. Acad. Sci. (1995).Google Scholar
2. Chinburg, T., Quaternionic exercises in K-theory Galois module structure. Proc.Great Lakes K-theory Conf., Fields Institute Conf. Series, Amer. Math. Soc. (1997).Google Scholar
3. Chinburg, T., Comparison of K-theory Galois module structure invariants. McMaster University, 9(1995– 1996), preprint.Google Scholar
4. Curtis, C.W. and Reiner, I., Methods of Representation Theory vols. I and II, Wiley, 1981. 1987.Google Scholar
5. Milnor, J.W., Introduction to Algebraic K-theory. Ann. Math. Studies 72, Princeton University Press, 1971.Google Scholar
6. Lang, S., Algebra. 2nd ed., Addison-Wesley, 1984.Google Scholar
7. Reiner, I., Maximal Orders. L. M. Soc. Monographs 5, Academic Press, 1975.Google Scholar
8. Snaith, V.P., Explicit Brauer Induction (with applications to algebra and number theory). Cambridge Studies in AdvancedMath. 40, Cambridge University Press, 1994.Google Scholar
9. Snaith, V.P., Galois Module Structure. Fields Institute Monographs, Amer. Math. Soc. 2(1994).Google Scholar
10. Snaith, V.P., Local fundamental classes derived from higher-dimensional K-groups. Proc. Great Lakes Ktheory Conf., Fields Institute Conf. Series, Amer. Math. Soc., (1997).Google Scholar
11. Snaith, V.P., Local fundamental classes derived from higher-dimensional K-groups II. Proc. Great Lakes K-theory Conf., Fields Institute Conf. Series, Amer. Math. Soc., (1997).Google Scholar