Research problem: Lipschitz properties of matrix group actions

Authors: Stephen J. Pierce; Leiba Rodman

Source: Linear and Multilinear Algebra, Volume 52, Number 6, November-December 2004 , pp. 461-466(6)

Publisher: Taylor and Francis Ltd

Buy & download fulltext article:

Price: $56.94 plus tax (Refund Policy)

Abstract:

Let G be a group of n × n matrices acting algebraically on an algebraic subset V of by x rArr

(A,x). Assume that I_n fixes every member of V. For a given x isin

V, let y be in the orbit of x in G. If y is close enough to x (with respect to some chosen norm) when there is an A isin

G with A suitably close to I_n such that y = phiv

(A,x)? These Lipschitz properties have been studied by the authors in several papers. If G is in addition a real analytic Lie group, then a relevant question concerns existence of analytic local cross sections. We give a discussion of these questions in this note and state some conjectures and unsolved problems.

Keywords: Congruence; Norms; Group action; Lipschitz properties; Analytic local cross sections; 2000 Mathematics Subject Classification: Primary 1; Secondary 15A60

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080410001697804

Publication date: 2004-11-01