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A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
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Timothée Marquis
Published/Copyright:
October 26, 2012
Abstract
We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable stabilisers of points. As an application, we deduce amongst other things that all topological one-parameter subgroups of a real or complex Kac–Moody group are obtained by exponentiating ad-locally finite elements of the corresponding Lie algebra.
Keywords: Lie groups; fixed point; buildings; locally compact groups; Kac–Moody groups; one-parameter subgroups
Funding source: F.R.S.-FNRS
Award Identifier / Grant number: Research Fellowship
I am very grateful to Pierre-Emmanuel Caprace for proposing this problem to me in the first place, as well as for various helpful comments and suggestions. I would also like to thank Tobias Hartnick and Ralf Köhl, as well as the anonymous referee for their useful comments.
Received: 2012-8-28
Revised: 2012-9-4
Published Online: 2012-10-26
Published in Print: 2015-1-1
© 2015 by De Gruyter
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- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
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- On embedding left-ordered groups into division rings
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Keywords for this article
Lie groups;
fixed point;
buildings;
locally compact groups;
Kac–Moody groups;
one-parameter subgroups
Articles in the same Issue
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
