Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 2, pp. 401--425 (2003)

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Invariant theory of a class of infinite-dimensional groups

Tuong Ton-That and Thai-Duong Tran

Tuong Ton-That
Department of Mathematics
University of Iowa
Iowa City, IA 52242
Thai-Duong Tran
Department of Computer Science
MCS \#560
Southwest Texas University
601 University Drive
San Marcos, TX 78666

Abstract: The representation theory of a class of infinite-di\-men\-sion\-al groups which are inductive limits of inductive systems of linear algebraic groups leads to a new invariant theory. In this article, we develop a coherent and comprehensive invariant theory of inductive limits of groups acting on inverse limits of modules, rings, or algebras. In this context, the {\it Fundamental Theorem of the Invariant Theory} is proved, a notion of {\it basis} of the rings of invariants is introduced, and a generalization of {\it Hilbert's Finiteness Theorem} is given. A generalization of some notions attached to the classical invariant theory such as {\it Hilbert's Nullstellensatz}, the primeness condition of the ideals of invariants are also discussed. Many examples of invariants of the infinite-dimensional classical groups are given.

Keywords: Invariant theory of inductive limits of groups acting on inverse limits of modules, rings, or algebras, Fundamental Theorem of Invariant Theory

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Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.

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