Tits Construction of The Exceptional Simple Lie Algebras
نویسندگان
چکیده
منابع مشابه
Tits Construction of the Exceptional Simple Lie Algebras
The classical Tits construction of the exceptional simple Lie algebras has been extended in a couple of directions by using either Jordan superalgebras or composition superalgebras. These extensions are reviewed here. The outcome has been the discovery of some new simple modular Lie superalgebras.
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The classical Tits construction provides models of the exceptional simple Lie algebras in terms of a unital composition algebra and a degree three simple Jordan algebra. A couple of actions of the symmetric group S4 on this construction are given. By means of these actions, the models provided by the Tits construction are related to models of the exceptional Lie algebras obtained from two diffe...
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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.
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولOn 1-dimensional Representations of Finite W -algebras Associated to Simple Lie Algebras of Exceptional Type
We consider the finite W -algebra U(g, e) associated to a nilpotent element e ∈ g in a simple complex Lie algebra g of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that U(g, e) always has a 1-dimensional representation, when g is of type G2, F4, E6 or E7. Thanks to a theorem of Premet, this allows one to deduce t...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2011
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2011.v7.n3.a4