Geodesic
Invariants of Lie algebras representable as semidirect sums with a~commutative ideal
Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1149-1164

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

Explicit formulae for invariants of the coadjoint representation are presented for Lie algebras that are semidirect sums of a classical semisimple Lie algebra with a commutative ideal with respect to a representation of minimal dimension or to a $k$th tensor power of such a representation. These formulae enable one to apply some known constructions of complete commutative families and to compare integrable systems obtained in this way. A completeness criterion for a family constructed by the method of subalgebra chains is suggested and a conjecture is formulated concerning the equivalence of the general Sadetov method and a modification of the method of shifting the argument, which was suggested earlier by Brailov. Bibliography: 12 titles.
Keywords: semisimple Lie algebras, commutative ideal, dynamical systems.
Mots-clés : invariants 
@article{SM_2009_200_8_a2,
     author = {A. S. Vorontsov},
     title = {Invariants of {Lie} algebras representable as semidirect sums with a~commutative ideal},
     journal = {Sbornik. Mathematics},
     pages = {1149--1164},
     publisher = {mathdoc},
     volume = {200},
     number = {8},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_8_a2/}
}
TY  - JOUR
AU  - A. S. Vorontsov
TI  - Invariants of Lie algebras representable as semidirect sums with a~commutative ideal
JO  - Sbornik. Mathematics
PY  - 2009
SP  - 1149
EP  - 1164
VL  - 200
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2009_200_8_a2/
LA  - en
ID  - SM_2009_200_8_a2
ER  - 
%0 Journal Article
%A A. S. Vorontsov
%T Invariants of Lie algebras representable as semidirect sums with a~commutative ideal
%J Sbornik. Mathematics
%D 2009
%P 1149-1164
%V 200
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2009_200_8_a2/
%G en
%F SM_2009_200_8_a2
A. S. Vorontsov. Invariants of Lie algebras representable as semidirect sums with a~commutative ideal. Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1149-1164. http://geodesic.mathdoc.fr/item/SM_2009_200_8_a2/