scholarly journals Finite order automorphisms and a parametrization of nilpotent orbits in p-adic lie algebras

2014 ◽  
Vol 136 (3) ◽  
pp. 551-598 ◽  
Author(s):  
Ricardo Portilla
Keyword(s):  
Lie Algebras ◽  
Finite Order ◽  
Nilpotent Orbits

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

scholarly journals Computing with Nilpotent Orbits in Simple Lie Algebras of Exceptional Type

2008 ◽  
Vol 11 ◽  
pp. 280-297 ◽  
Author(s):  
Willem A. de Graaf
Keyword(s):  
Algebraic Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Simple Algorithm ◽  
Adjoint Action ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Simple Algebraic Group ◽  
Algebraically Closed Field ◽  
Simple Lie Algebras

AbstractLet G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a representative of a nilpotent orbit. We use this to compute lists of representatives of these orbits for the Lie algebras of exceptional type. Then we give two applications. The first one concerns settling a conjecture by Elashvili on the index of centralizers of nilpotent orbits, for the case where the Lie algebra is of exceptional type. The second deals with minimal dimensions of centralizers in centralizers.

ON SEMIREGULAR NILPOTENT ORBITS IN SIMPLE LIE ALGEBRAS OF TYPE D

2002 ◽  
Vol 01 (03) ◽  
pp. 341-356 ◽  
Author(s):  
BENOÎT ARBOUR ◽  
DRAGOMIR Ž. ĐOKOVIĆ
Keyword(s):  
Linear Combination ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Nilpotent Orbits ◽  
Connected Component ◽  
Real Form ◽  
Simple Complex ◽  
Type D ◽  
Explicit Formulae

We derive explicit formulae for the characteristics H(k) of the semiregular nilpotent orbits Dn(ak) of the simple complex Lie algebra [Formula: see text] of type Dn. These formulae express H(k) as an integral linear combination of a basis of the Cartan subalgebra [Formula: see text] of [Formula: see text]. For that purpose we use several suitable bases of [Formula: see text] consisting of coroots. We also construct several explicit standard triples (E, H, F) with H = H(k), and E, F ∈ Dn(ak). Similar triples are constructed also for each connected component of the intersection of the orbit Dn(ak) with the split real form [Formula: see text] and the real form [Formula: see text] of [Formula: see text].

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