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

B. Es Saadi, Yu. Khakimdjanov, A. Makhlouf (2003)

Annales mathématiques Blaise Pascal

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...

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