Isomorphisms of Kac-Moody groups which preserve bounded subgroups.

DOI10.1016/j.aim.2005.08.008zbMath1152.20029arXivmath/0506535OpenAlexW2004869818MaRDI QIDQ850070

Pierre-Emmanuel Caprace, Bernhard Mühlherr

Publication date: 15 November 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506535

zbMATH Keywords

Chevalley groupsisomorphism problemstandard automorphismsKac-Moody groupstwin buildingsbounded subgroupsroot datafinite-type parabolic subgroupsLevi decompositionsMoufang property

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Automorphisms of infinite groups (20E36) Buildings and the geometry of diagrams (51E24) Groups with a (BN)-pair; buildings (20E42)

Related Items

Local-global invariants of finite and infinite groups: around Burnside from another side., 3-spherical twin buildings, Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds, Abstract involutions of algebraic groups and of Kac–Moody groups, A uniform bound on the nilpotency degree of certain subalgebras of Kac-Moody algebras, The sphericity of the Phan geometries of type $B_n$ and $C_n$ and the Phan-type theorem of type $F_4$, Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups., Algebraic ℚ-groups as abstract groups, Isomorphisms of unitary forms of Kac-Moody groups over finite fields, Simplicity and superrigidity of twin building lattices.

Cites Work

• Uniqueness and presentation of Kac-Moody groups over fields
• Homomorphismes abstraits de groupes algébriques simples
• On automorphisms of Kac-Moody algebras and groups
• Hyperbolic Kac-Moody buildings, nonisomorphic groups with the same building.
• Isomorphisms of Kac-Moody groups
• Twin buildings and applications to \(S\)-arithmetic groups
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