Geodesic
Invariant Theory of a Class of Infinite-Dimensional Groups
Journal of Lie theory, Tome 13 (2003) no. 2, pp. 401-425 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JLT_2003_13_2_JLT_2003_13_2_a5,
     author = {T. Ton-That and T.-D. 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/JLT_2003_13_2_JLT_2003_13_2_a5/}
}
TY  - JOUR
AU  - T. Ton-That
AU  - T.-D. Tran 
TI  - Invariant Theory of a Class of Infinite-Dimensional Groups
JO  - Journal of Lie theory
PY  - 2003
SP  - 401
EP  - 425
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a5/
ID  - JLT_2003_13_2_JLT_2003_13_2_a5
ER  - 
%0 Journal Article
%A T. Ton-That
%A T.-D. Tran 
%T Invariant Theory of a Class of Infinite-Dimensional Groups
%J Journal of Lie theory
%D 2003
%P 401-425
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a5/
%F JLT_2003_13_2_JLT_2003_13_2_a5
T. Ton-That; T.-D. 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/JLT_2003_13_2_JLT_2003_13_2_a5/