Geodesic
Various representations of matrix Lie algebras related to homogeneous surfaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 42-60

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

We construct a $3$-parameter family of real homogeneous hypersurfaces in a $3$-dimensional complex space. This family generalizes several examples that were published earlier. It contains both Levi nondegenerate surfaces (strictly pseudoconvex and indefinite ones) and surfaces with degenerate Levi form. Unlike the known cumbersome descriptions of matrix algebras corresponding to the surfaces under consideration, we propose an upper triangular representation of these algebras with simple special bases. We show that all affinely homogeneous surfaces of the constructed family are algebraic ones of degree $1,2,3,4$, or $6$.
Keywords: homogeneous manifold, complex space, real hypersurface, vector field.
Mots-clés : matrix Lie algebra 
@article{IVM_2013_4_a4,
     author = {A. V. Loboda and V. K. Evchenko},
     title = {Various representations of matrix {Lie} algebras related to homogeneous surfaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--60},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_4_a4/}
}
TY  - JOUR
AU  - A. V. Loboda
AU  - V. K. Evchenko
TI  - Various representations of matrix Lie algebras related to homogeneous surfaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 42
EP  - 60
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_4_a4/
LA  - ru
ID  - IVM_2013_4_a4
ER  - 
%0 Journal Article
%A A. V. Loboda
%A V. K. Evchenko
%T Various representations of matrix Lie algebras related to homogeneous surfaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 42-60
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_4_a4/
%G ru
%F IVM_2013_4_a4
A. V. Loboda; V. K. Evchenko. Various representations of matrix Lie algebras related to homogeneous surfaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 42-60. http://geodesic.mathdoc.fr/item/IVM_2013_4_a4/