Linear Lie algebras with finite dimensional centralizers

2001/06/30 by G. Gaeta, S. Walcher
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP #msc:34C14 #msc:34A05 #msc:22E05

paper · pdf

published as J. Math. Anal. Appl. 269 (2002), 578-587 · 10 pages; revised version to appear in J. Math. Anal. Appl

arxiv created 2001/11/19 · arxiv updated 2009/11/30

Abstract

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario some applications to normal forms and to certain equations with fundamental solutions are presented.

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