Induction theorems on the stable rationality

of the center of the ring of generic matrices

Author:
Esther Beneish

Journal:
Trans. Amer. Math. Soc. **350** (1998), 3571-3585

MSC (1991):
Primary 13A50, 20C10

DOI:
https://doi.org/10.1090/S0002-9947-98-02202-8

MathSciNet review:
1475675

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Abstract | References | Similar Articles | Additional Information

Abstract: Following Procesi and Formanek, the center of the division ring of generic matrices over the complex numbers is stably equivalent to the fixed field under the action of , of the function field of the group algebra of a -lattice, denoted by . We study the question of the stable rationality of the center over the complex numbers when is a prime, in this module theoretic setting. Let be the normalizer of an -sylow subgroup of . Let be a -lattice. We show that under certain conditions on , induction-restriction from to does not affect the stable type of the corresponding field. In particular, and are stably isomorphic and the isomorphism preserves the -action. We further reduce the problem to the study of the localization of at the prime ; all other primes behave well. We also present new simple proofs for the stable rationality of over , in the cases and .

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Additional Information

**Esther Beneish**

Affiliation:
Department of Mathematics, University of Wisconsin-Parkside, Kenosha, Wisconsin 53141-2000

DOI:
https://doi.org/10.1090/S0002-9947-98-02202-8

Received by editor(s):
September 22, 1996

Article copyright:
© Copyright 1998
American Mathematical Society