scholarly journals Nilpotent orbits and mixed gradings of semisimple Lie algebras

2021 ◽  
Author(s):  
Dmitri I. Panyushev
Keyword(s):  
Lie Algebras ◽  
Nilpotent Orbits ◽  
Semisimple Lie Algebras

Decomposition Varieties in Semisimple Lie Algebras

1998 ◽  
Vol 50 (5) ◽  
pp. 929-971 ◽  
Author(s):  
Abraham Broer
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Orbits ◽  
Semisimple Lie Algebra ◽  
Semisimple Lie Algebras ◽  
Rational Singularities ◽  
Common Generalization ◽  
Simultaneous Resolution ◽  
Decomposition Class

AbstractThe notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.

Nilpotent Orbits in Semisimple Lie Algebras

2017 ◽  
Author(s):  
David H. Collingwood ◽  
William M. McGovern
Keyword(s):  
Lie Algebras ◽  
Nilpotent Orbits ◽  
Semisimple Lie Algebras

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

Semisimple Lie Algebras of Operators

2001 ◽  
pp. 181-202
Author(s):  
Daniel Beltiţă ◽  
Mihai Şabac
Keyword(s):  
Lie Algebras ◽  
Semisimple 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.

Semisimple Lie Algebras

2020 ◽  
pp. 71-134
Author(s):  
Morikuni Goto ◽  
Frank D. Grosshans
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras

Glider representations of a chain of semisimple Lie algebras

2019 ◽  
pp. 153-178
Author(s):  
Frederik Caenepeel ◽  
Fred Van Oystaeyen
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
A Chain
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