Property (T) for groups graded by root systems

Details Property (T) for groups graded by root systems Property (T) for groups graded by root systems

2011-01-31

arxiv.org/abs/1102.0031v1

Mathematics

Group Theory

78 pages

Scientific paper

We introduce and study the class of groups graded by root systems. We prove that if {\Phi} is an irreducible classical root system of rank at least 2 and G is a group graded by {\Phi}, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of G. As the main application of this result we prove that for any reduced irreducible classical root system {\Phi} of rank at least 2 and a finitely generated commutative ring R with 1, the Steinberg group St_{\Phi}(R) and the elementary Chevalley group E_{\Phi}(R) have property (T).

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