Maximal subalgebras of Cartan type in the exceptional Lie algebras

DOI10.1007/s00029-015-0199-5zbMath1375.17012arXiv1409.3861OpenAlexW2962869504MaRDI QIDQ268170

Sebastian Herpel, David I. Stewart

Publication date: 14 April 2016

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3861

zbMATH Keywords

irreducible representationWitt algebranilpotent elementsimple Lie algebra\(p\)-subalgebraexceptional simple Lie algebra of classical typegood characteristicmaximal subalgebranon-graded Hamiltonian Lie algebraregular nilpotent element

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Structure theory for Lie algebras and superalgebras (17B05) Exceptional (super)algebras (17B25) Lie algebras of linear algebraic groups (17B45) Modular Lie (super)algebras (17B50)

Related Items

A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebras ⋮ Some special features of Cayley algebras, and \(G_2\), in low characteristics ⋮ The Restricted Ermolaev Algebra and F₄ ⋮ Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic ⋮ Varieties of elementary abelian Lie algebras and degrees of modules

Uses Software

• GAP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the smoothness of normalisers, the subalgebra structure of modular Lie algebras, and the cohomology of small representations
• Restricted Lie algebras with maximal 0-PIM
• Graded modules of graded Lie algebras of Cartan type. III: Irreducible modules
• \(\text{Ext}^1\)-quivers for the Witt algebra \(W(1,1)\)
• A construction of certain maximal subgroups of the algebraic groups \(E_ 6\) and \(F_ 4\)
• Simple restricted modules for the restricted Hamiltonian algebra
• Maximal subalgebras of simple modular Lie algebras
• Optimal \(\text{SL}(2)\)-homomorphisms.
• Über Wittsche Lie-Ringe
• Sur les groupes de Lie algébriques sur un corps de caractéristique \(p > 0\)
• Closed orbits and uniform $S$-instability in geometric invariant theory
• Irreducible almost simple subgroups of classical algebraic groups
• Centres of centralizers of unipotent elements in simple algebraic groups
• EXTENSIONS OF THE WITT ALGEBRA AND APPLICATIONS
• The maximal subgroups of classical algebraic groups
• Irreducible subgroups of exceptional algebraic groups
• Maximal subgroups of exceptional algebraic groups
• [https://portal.mardi4nfdi.de/wiki/Publication:4031442 The Construction of the Maximal A 1 � S in the Exceptional Algebraic Groups]
• RIGID ORBITS AND SHEETS IN REDUCTIVE LIE ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC
• The maximal subgroups of positive dimension in exceptional algebraic groups
• Jordan block sizes of unipotent elements in exceptional algebraic groups
• An Analogue of the Jacobson-Morozov Theorem for Lie Algebras of Reductive Groups of Good Characteristics
• Algebraic groups and modular Lie algebras
• Simple Lie algebras over fields of positive characteristic. II: Classifying the absolute toral rank two case
• Simple Lie algebras over fields of positive characteristic. I: Structure theory