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Hecke Algebras and Class-Group Invariants

  • V. P. Snaith

Abstract

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.

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References

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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).
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).
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4. Curtis, C.W. and Reiner, I., Methods of Representation Theory vols. I and II, Wiley, 1981. 1987.
5. Milnor, J.W., Introduction to Algebraic K-theory. Ann. Math. Studies 72, Princeton University Press, 1971.
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7. Reiner, I., Maximal Orders. L. M. Soc. Monographs 5, Academic Press, 1975.
8. Snaith, V.P., Explicit Brauer Induction (with applications to algebra and number theory). Cambridge Studies in AdvancedMath. 40, Cambridge University Press, 1994.
9. Snaith, V.P., Galois Module Structure. Fields Institute Monographs, Amer. Math. Soc. 2(1994).
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).
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).
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Hecke Algebras and Class-Group Invariants

  • V. P. Snaith

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