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The effect of an involution in\(\widetilde{K}^0 \) (ZG)

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Abstract

The involution in the Grothendieck group of the group ring of a finite cyclic group of prime order p, induced by the transition to the contragredient module is identical to complex conjugation followed by the automorphism x → x−1 in the ideal class group of the cyclotomic field of order p.

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Literature cited

  1. C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, New York (1962).

  2. G. Swan, “Induced representations and projective modules,” Ann. of Math.,71, No. 3 (1960).

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, USA

    I. Reiner

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  1. I. Reiner
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Russian article translated from the English by V. L. Golo.

Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 523–528, May, 1968.

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Reiner, I. The effect of an involution in\(\widetilde{K}^0 \) (ZG). Mathematical Notes of the Academy of Sciences of the USSR 3, 333–336 (1968). https://doi.org/10.1007/BF01150984

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  • DOI: https://doi.org/10.1007/BF01150984

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