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Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups. (English) Zbl 1206.20046

Let \(X\) be an irreducible building that is neither spherical nor affine. The authors show that every sufficiently large automorphism group \(G\) of \(X\) admits many non-trivial quasi-morphisms \(G\to\mathbb{R}\). Applied to Kac-Moody groups over integral domains, this yields examples of finitely presented simple groups with infinite commutator width; compare A. Muranov [Int. J. Algebra Comput. 17, No. 3, 607-659 (2007; Zbl 1141.20022)].

MSC:

20F65 Geometric group theory
20E42 Groups with a \(BN\)-pair; buildings
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
20E32 Simple groups

Citations:

Zbl 1141.20022
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References:

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