Abstract involutions of algebraic groups and of Kac–Moody groups

DOI10.1515/JGT.2010.033zbMath1234.20037arXiv0905.1280OpenAlexW2020872878MaRDI QIDQ3007959

Max Horn, Ralf Köhl (né Gramlich), Bernhard Mühlherr

Publication date: 17 June 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.1280

zbMATH Keywords

algebraic groupsCoxeter groupsroot systemsKac-Moody groupstwin buildingstwisted involutionsdouble coset decompositionsRGD-systems

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Buildings and the geometry of diagrams (51E24) Groups with a (BN)-pair; buildings (20E42) Kac-Moody groups (20G44)

Related Items

On flips of unitary buildings I: Classification of flips, Buildings and Kac-Moody Groups, Curtis-Tits groups of simply-laced type, Curtis-Tits groups generalizing Kac-Moody groups of type \(\widetilde A_{n-1}\)., The combinatorics of automorphisms and opposition in generalised polygons, Infinite generation of non-cocompact lattices on right-angled buildings., Lattices in complete rank 2 Kac-Moody groups., Expander graphs from Curtis-Tits groups., AUTOMORPHISMS AND OPPOSITION IN TWIN BUILDINGS

Cites Work

• Uniqueness and presentation of Kac-Moody groups over fields
• Covering theory for graphs of groups
• Homomorphismes abstraits de groupes algébriques simples
• Isomorphisms of Kac-Moody groups which preserve bounded subgroups.
• Twisted identities in Coxeter groups.
• On automorphisms of Kac-Moody algebras and groups
• The orbits of affine symmetric spaces under the action of minimal parabolic subgroups
• Cohomology of buildings and of their automorphism groups.
• On the classification of \(k\)-involutions
• Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces
• On rationality properties of involutions of reductive groups
• Groupes reductifs
• Endliche Erzeugbarkeit arithmetischer Gruppen über Funktionenkörpern
• Reductive groups over a local field
• Conjugacy classes of involutions in Coxeter groups
• The combinatorics of twisted involutions in Coxeter groups
• The Structure of Semisimple Symmetric Spaces
• Locally split and locally finite twin buildings of 2-spherical type
• A new proof of a theorem of Phan
• On the simple connectedness of certain subsets of buildings