Geodesic
Invariant Theory of a Class of Infinite-Dimensional Groups
Tuong Ton-That1 ; Thai-Duong Tran2, 3, 4, 5, 6, 7, 8, 9, 10
1Dept. of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A.
2Dept. of Computer Science, Southwest Texas University, 601 University Drive, San Marcos, TX 78666, U.S.A.
3The representation theory of a class of infinite-dimensional 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
4is proved, a notion of
5of the rings of invariants is introduced, and a generalization of
6is given. A generalization of some notions attached to the classical invariant theory such as Hilbert's
7, the primeness condition of the ideals of invariants are also discussed. Many examples of invariants of the infinite-dimensional classical groups are given.
8Keywords: Invariant theory, inductive limits, groups acting on inverse limits of modules, rings, algebras, Fundamental Theorem of Invariant Theory.
9MSC: 13A50; 22E65, 13F20
10[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 401-425

Voir la notice de l'article provenant de la source Heldermann Verlag

The representation theory of a class of infinite-dimensional 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 Fundamental Theorem of the Invariant Theory is proved, a notion of basis of the rings of invariants is introduced, and a generalization of Hilbert's Finiteness Theorem is given. A generalization of some notions attached to the classical invariant theory such as 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.
Classification : 13A50, 22E65, 13F20
Mots-clés : Invariant theory, inductive limits, groups acting on inverse limits of modules, rings, algebras, Fundamental Theorem of Invariant Theory

Tuong Ton-That  1   ; Thai-Duong Tran  2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10

1 Dept. of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A.
2 Dept. of Computer Science, Southwest Texas University, 601 University Drive, San Marcos, TX 78666, U.S.A.
3 The representation theory of a class of infinite-dimensional 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
4 is proved, a notion of
5 of the rings of invariants is introduced, and a generalization of
6 is given. A generalization of some notions attached to the classical invariant theory such as Hilbert's
7 , the primeness condition of the ideals of invariants are also discussed. Many examples of invariants of the infinite-dimensional classical groups are given.
8 Keywords: Invariant theory, inductive limits, groups acting on inverse limits of modules, rings, algebras, Fundamental Theorem of Invariant Theory.
9 MSC: 13A50; 22E65, 13F20
10 [ 
Tuong Ton-That; Thai-Duong Tran. Invariant Theory of a Class of Infinite-Dimensional Groups. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 401-425. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a5/
@article{JOLT_2003_13_2_a5,
     author = {Tuong Ton-That and Thai-Duong Tran},
     title = {Invariant {Theory} of a {Class} of {Infinite-Dimensional} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {401--425},
     year = {2003},
     volume = {13},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a5/}
}
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