Lattice invariants and the center of the generic division ring

Author:
Esther Beneish

Journal:
Trans. Amer. Math. Soc. **356** (2004), 1609-1622

MSC (2000):
Primary 20C10, 16R30, 13A50, 16K20

DOI:
https://doi.org/10.1090/S0002-9947-03-03331-2

Published electronically:
October 21, 2003

MathSciNet review:
2034321

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite group, let be a -lattice, and let be a field of characteristic zero containing primitive roots of 1. Let be the quotient field of the group algebra of the abelian group . It is well known that if is quasi-permutation and -faithful, then is stably equivalent to . Let be the center of the division ring of generic matrices over . Let be the symmetric group on symbols. Let be a prime. We show that there exist a split group extension of by a -elementary group, a -faithful quasi-permutation -lattice , and a one-cocycle in such that is stably isomorphic to . This represents a reduction of the problem since we have a quasi-permutation action; however, the twist introduces a new level of complexity. The second result, which is a consequence of the first, is that, if is algebraically closed, there is a group extension of by an abelian -group such that is stably equivalent to the invariants of the Noether setting .

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Additional Information

**Esther Beneish**

Affiliation:
Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859

Email:
benei1e@cmich.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03331-2

Received by editor(s):
May 13, 2002

Received by editor(s) in revised form:
March 7, 2003

Published electronically:
October 21, 2003

Additional Notes:
This work was partially supported by NSF grant #DMS-0070665

Article copyright:
© Copyright 2003
American Mathematical Society