Geodesic
Some direct limits of the classical Lie algebras and the projective limits connected with them
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1069-1084 
I. A. Yanson. Some direct limits of the classical Lie algebras and the projective limits connected with them. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1069-1084. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a15/
@article{FPM_1995_1_4_a15,
     author = {I. A. Yanson},
     title = {Some direct limits of the classical {Lie} algebras and the projective limits connected with them},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1069--1084},
     year = {1995},
     volume = {1},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a15/}
}
TY  - JOUR
AU  - I. A. Yanson
TI  - Some direct limits of the classical Lie algebras and the projective limits connected with them
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1995
SP  - 1069
EP  - 1084
VL  - 1
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a15/
LA  - ru
ID  - FPM_1995_1_4_a15
ER  - 
%0 Journal Article
%A I. A. Yanson
%T Some direct limits of the classical Lie algebras and the projective limits connected with them
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1995
%P 1069-1084
%V 1
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a15/
%G ru
%F FPM_1995_1_4_a15

Voir la notice de l'article provenant de la source Math-Net.Ru

The present article considers some concrete classes of direct limits of the classical simple Lie algebras of the types A, B, C, D. With each such direct limit one can connect the projective limit of sets of dominant integral weights, the projective limit of the invariants of joint action in the algebras of the polynomial functions and sometimes the projective limit of the root lattices. The article is devoted to the study of structural mappings in these projective limits and to the proof of non-triviality of the latters.

[1] Zh. Diksme, Universalnye obertyvayuschie algebry, M., 1978

[2] Yu. Bahturin, G. Benkart, “Highest weight modules over locally finite Lie algebras” (to appear)

[3] N. Burbaki, Gruppy i algebry Li, M., 1978 | MR