Lattice invariants and the center of the generic division ring
Author:
Esther Beneish
Journal:
Trans. Amer. Math. Soc. 356 (2004), 16091622
MSC (2000):
Primary 20C10, 16R30, 13A50, 16K20
Published electronically:
October 21, 2003
MathSciNet review:
2034321
Fulltext PDF Free Access
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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 quasipermutation 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 quasipermutation lattice , and a onecocycle in such that is stably isomorphic to . This represents a reduction of the problem since we have a quasipermutation 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:
http://dx.doi.org/10.1090/S0002994703033312
PII:
S 00029947(03)033312
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 #DMS0070665
Article copyright:
© Copyright 2003
American Mathematical Society
