Geodesic
Characterization of Simple Highest Weight Modules
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 606-614

Voir la notice de l'article provenant de la source Cambridge

DOI

We prove that for simple complex finite dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, and the Heisenberg–Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro algebras and for Heisenberg algebras.
DOI : 10.4153/CMB-2011-199-5
Mots-clés : 17B20, 17B65, 17B66, 17B68, Lie algebra, highest weight module, triangular decomposition, locally nilpotent action 
Mazorchuk, Volodymyr; Zhao, Kaiming. Characterization of Simple Highest Weight Modules. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 606-614. doi: 10.4153/CMB-2011-199-5
@article{10_4153_CMB_2011_199_5,
     author = {Mazorchuk, Volodymyr and Zhao, Kaiming},
     title = {Characterization of {Simple} {Highest} {Weight} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {606--614},
     year = {2013},
     volume = {56},
     number = {3},
     doi = {10.4153/CMB-2011-199-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-199-5/}
}
TY  - JOUR
AU  - Mazorchuk, Volodymyr
AU  - Zhao, Kaiming
TI  - Characterization of Simple Highest Weight Modules
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 606
EP  - 614
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-199-5/
DO  - 10.4153/CMB-2011-199-5
ID  - 10_4153_CMB_2011_199_5
ER  - 
%0 Journal Article
%A Mazorchuk, Volodymyr
%A Zhao, Kaiming
%T Characterization of Simple Highest Weight Modules
%J Canadian mathematical bulletin
%D 2013
%P 606-614
%V 56
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-199-5/
%R 10.4153/CMB-2011-199-5
%F 10_4153_CMB_2011_199_5

Cité par Sources :