On the Cayley degree of an algebraic group
Algebraic Geometry
2009-07-06 v1 Group Theory
Abstract
A connected linear algebraic group G is called a Cayley group if the Lie algebra of G endowed with the adjoint G-action and the group variety of G endowed with the conjugation G-action are birationally G-isomorphic. In particular, the classical Cayley map, X \mapsto (I_n-X)/(I_n+X), between the special orthogonal group SO_n and its Lie algebra so_n, shows that SO_n is a Cayley group. In an earlier paper (see math.AG/0409004) we classified the simple Cayley groups defined over an algebraically closed field of characteristic zero. Here we consider a new numerical invariant of G, the Cayley degree, which "measures" how far G is from being Cayley, and prove upper bounds on Cayley degrees of some groups.
Cite
@article{arxiv.math/0608473,
title = {On the Cayley degree of an algebraic group},
author = {Nicole Lemire and Vladimir L. Popov and Zinovy Reichstein},
journal= {arXiv preprint arXiv:math/0608473},
year = {2009}
}
Comments
LaTEX, 8 pages