Journal of Lie Theory Vol. 13, No. 2, pp. 401425 (2003) 

Invariant theory of a class of infinitedimensional groupsTuong TonThat and ThaiDuong TranTuong TonThatDepartment of Mathematics University of Iowa Iowa City, IA 52242 USA tonthat@math.uiowa.edu and ThaiDuong Tran Department of Computer Science MCS \#560 Southwest Texas University 601 University Drive San Marcos, TX 78666 USA tt10@swt.edu Abstract: The representation theory of a class of infinitedi\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 infinitedimensional 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 Full text of the article:
Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.
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