Geodesic
On Diverse Forms of Homogeneity of Lie Algebras
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 178-192.

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

In the paper, several different ways to introduce the notion of homogeneity in the case of finite-dimensional Lie algebras are considered. Among these notions, we have homogeneity, almost homogeneity, weak homogeneity, and projective homogeneity. Constructions and examples of Lie algebras of diverse forms of homogeneity are presented. It is shown that the notions of weak homogeneity and of weak projective homogeneity are the most nontrivial and interesting for a detailed investigation. Some structural properties are proved for weakly homogeneous and weakly projectively homogeneous Lie algebras.
Keywords: Lie algebra, almost homogeneity, weak homogeneity, projective homogeneity, weak projective homogeneity, Engel theorem, nilpotent algebra
Mots-clés : Cartan subalgebra. 
@article{MZM_2010_88_2_a2,
     author = {V. V. Gorbatsevich},
     title = {On {Diverse} {Forms} of {Homogeneity} of {Lie} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {178--192},
     publisher = {mathdoc},
     volume = {88},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a2/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On Diverse Forms of Homogeneity of Lie Algebras
JO  - Matematičeskie zametki
PY  - 2010
SP  - 178
EP  - 192
VL  - 88
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a2/
LA  - ru
ID  - MZM_2010_88_2_a2
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On Diverse Forms of Homogeneity of Lie Algebras
%J Matematičeskie zametki
%D 2010
%P 178-192
%V 88
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a2/
%G ru
%F MZM_2010_88_2_a2
V. V. Gorbatsevich. On Diverse Forms of Homogeneity of Lie Algebras. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 178-192. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a2/

[1] A. I. Kostrikin, “Ob odnorodnykh algebrakh”, Izv. AN SSSR. Ser. matem., 29:2 (1965), 471–484 | MR | Zbl

[2] M. Stroppel, “Homogeneous locally compact groups”, J. Algebra, 199:2 (1998), 528–543 | MR | Zbl

[3] N. Burbaki, Gruppy i algebry Li. Algebry Li, svobodnye algebry Li i gruppy Li, Elementy matematiki, Mir, M., 1976 | MR | Zbl

[4] S. Świerczkowski, “Homogeneous Lie algebras”, Bull. Austral. Math. Soc., 4 (1971), 349–353 | MR | Zbl

[5] D. Z̆. Djoković, “Real homogeneous algebras”, Proc. Amer. Math. Soc., 41:2 (1973), 457–462 | MR | Zbl

[6] N. Dzhekobson, Algebry Li, Mir, M., 1964 | MR | Zbl

[7] H. Mäurer, M. Stroppel, “Groups that are almost homogeneous”, Geom. Dedicata, 68:2 (1997), 229–243 | MR | Zbl

[8] M. Stroppel, “Homogeneous symplectic maps and almost homogeneous Heisenberg groups”, Forum Math., 11:6 (1999), 659–672 | MR | Zbl

[9] M.-P. Gong, Classification of nilpotent Lie algebras of dimension 7, Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1998

[10] Yu. B. Khakimdzhanov, “O differentsirovaniyakh nekotorykh nilpotentnykh algebr Li”, Izv. vuzov. Matem., 1976, no. 1, 100–110 | MR | Zbl

[11] E. B. Vinberg, V. V. Gorbatsevich, A. L. Onischik, “Stroenie grupp i algebr Li”, Gruppy Li i algebry Li – 3, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 41, VINITI, M., 1990, 5–253 | MR | Zbl

[12] A. Borel, Lineinye algebraicheskie gruppy, Mir, M., 1972 | MR | Zbl

[13] A. L. Onischik, “Razlozheniya reduktivnykh grupp Li”, Matem. sb., 80:4 (1969), 553–599 | MR | Zbl