Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration

Es Saadi, B., Khakimdjanov, Yu., and Makhlouf, A.. "Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration." Annales mathématiques Blaise Pascal 10.2 (2003): 315-326. <http://eudml.org/doc/10493>.

@article{EsSaadi2003,
abstract = {The aim of this work is to enumerate the standard subalgebras of a semisimple Lie algebra. The computations are based on the approach developed by Yu. Khakimdjanov in 1974. In this paper, we give a general formula for the number of standard subalgebras not necessarly nilpotent of a semisimple Lie algebra of type A$_\{p\}$ and the exceptional semisimple Lie algebras. With computer aided, we enumerate this number for the other types of small rank. Therefore, We deduce the number in the nilpotent case and describe a family of complete nilpotent standard subalgebras, these algebras are the nilradical of their normalizer.},
affiliation = {Université de Haute Alsace Laboratoire de Mathématiques et Applications 4, rue des Frères Lumière 68093 Mulhouse Cedex FRANCE; Université de Haute Alsace Laboratoire de Mathématiques et Applications 4, rue des Frères Lumière 68093 Mulhouse Cedex FRANCE; Université de Haute Alsace Laboratoire de Mathématiques et Applications 4, rue des Frères Lumière 68093 Mulhouse Cedex FRANCE},
author = {Es Saadi, B., Khakimdjanov, Yu., Makhlouf, A.},
journal = {Annales mathématiques Blaise Pascal},
keywords = {parabolic subalgebra; conjugacy classes},
language = {eng},
month = {7},
number = {2},
pages = {315-326},
publisher = {Annales mathématiques Blaise Pascal},
title = {Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration},
url = {http://eudml.org/doc/10493},
volume = {10},
year = {2003},
}

TY - JOUR
AU - Es Saadi, B.
AU - Khakimdjanov, Yu.
AU - Makhlouf, A.
TI - Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration
JO - Annales mathématiques Blaise Pascal
DA - 2003/7//
PB - Annales mathématiques Blaise Pascal
VL - 10
IS - 2
SP - 315
EP - 326
AB - The aim of this work is to enumerate the standard subalgebras of a semisimple Lie algebra. The computations are based on the approach developed by Yu. Khakimdjanov in 1974. In this paper, we give a general formula for the number of standard subalgebras not necessarly nilpotent of a semisimple Lie algebra of type A$_{p}$ and the exceptional semisimple Lie algebras. With computer aided, we enumerate this number for the other types of small rank. Therefore, We deduce the number in the nilpotent case and describe a family of complete nilpotent standard subalgebras, these algebras are the nilradical of their normalizer.
LA - eng
KW - parabolic subalgebra; conjugacy classes
UR - http://eudml.org/doc/10493
ER -