English

A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces

Algebraic Geometry 2007-05-23 v2

Abstract

It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra techniques. The algorithm has been implemented in Magma.

Keywords

Cite

@article{arxiv.math/0501157,
  title  = {A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces},
  author = {Willem A. de Graaf and Michael Harrison and Jana Pilnikova and Josef Schicho},
  journal= {arXiv preprint arXiv:math/0501157},
  year   = {2007}
}

Comments

16 pages some minor revisions

R2 v1 2026-07-22T17:14:22.918Z