Submission date: 17 October 2007

Abstract:

We investigate the theory of pseudo-finite dimensional representations of the Lie algebra sl_2 k, where k is an algebraically closed field of characteristic 0. Our principal contribution is to bring out a connection to fundamental problems in the diophantine geometry of curves. We expect to show, in a subsequent paper, that the theory of pseudo-finite dimensional representations of sl_2 k is decidable, modulo some widely believed conjectures in diophantine geometry.

Mathematics Subject Classification: 03C60

Keywords and phrases: Pseudo-finite dimensional representations, von Neumann rings, decidable theories.

Full text: pdf, dvi, ps.