Computing with Nilpotent Orbits in Simple Lie Algebras of Exceptional Type
نویسندگان
چکیده
منابع مشابه
Classification of Admissible Nilpotent Orbits in Simple Exceptional Real Lie Algebras of Inner Type
In this paper we give a classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie groups of inner type. We use a lemma of Takuya Ohta and some information from the work of Dragomir Djoković to construct a simple algorithm which allows us to decide the admissiblity of a given orbit.
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In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
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Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
متن کاملClassification of Admissible Nilpotent Orbits in Simple Real Lie Algebras E6(6) and E6(−26)
This paper completes the classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie algebras. The author has previoulsly determined such orbits for exceptional real simple Lie algebras of inner type. Here he uses the same techniques, with some modifications, to classify the admissible nilpotent orbits of E6(6) and E6(−26) under their simply connected Lie groups.
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2008
ISSN: 1461-1570
DOI: 10.1112/s1461157000000607