Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration
Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 315-326.

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.

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     author = {Es Saadi, B. and Khakimdjanov, Yu. and Makhlouf, A.},
     title = {Standard {Subalgebras} of {Semisimple} {Lie} {Algebras} and {Computer-Aided} for {Enumeration}},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {315--326},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {10},
     number = {2},
     year = {2003},
     doi = {10.5802/ambp.180},
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     zbl = {1107.17005},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.180/}
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Es Saadi, B.; Khakimdjanov, Yu.; Makhlouf, A. Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration. Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 315-326. doi : 10.5802/ambp.180. http://www.numdam.org/articles/10.5802/ambp.180/

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