The center of the generic division ring and
twisted multiplicative group actions


Esther Beneish
Department of Mathematics	
Eastern Washington University
Cheney,  WA 99004		


Abstract:

    The problem we study is whether the center Cn, of the division ring of nxn generic  matrices  is stably  rational  over the base field F.
     Let Sp be the Symmetric group on p letters for a prime p. Let H be a p-Sylow subgroup of Sp. Let I denote induction-restriction from H to Sp. Let A be the root lattice. We show that there is a rational extension field L of F, a one-cocycle a from I(A) to L*, and an action of Sp, twisted by a, on L(I(A)) such that the center Cp is stably isomorphic to the fixed field of L(I(A)).  The cocycle a corresponds to an element of the relative Brauer group of L over its fixed field under the action of H.  Furthermore the fixed field of L under the action of Sp is stably rational over F.

Status:  Preprint.