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Property $t$ for Groups Graded by Root Systems (Memoirs of the American Mathematical Society) PDF

148 Pages·2017·1.2 MB·English
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by Mikhail Ershov| 2017| 148 pages| 1.2| English

About Property $t$ for Groups Graded by Root Systems (Memoirs of the American Mathematical Society)

The authors introduce and study the class of groups graded by root systems. They prove that if $Phi$ is an irreducible classical root system of rank $geq 2$ 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 theorem the authors prove that for any reduced irreducible classical root system $Phi$ of rank $geq 2$ and a finitely generated commutative ring $R$ with $1$, the Steinberg group $mathrm StPhi(R)$ and the elementary Chevalley group $mathbb EPhi(R)$ have property $(T)$. They also show that there exists a group with property $(T)$ which maps onto all finite simple groups of Lie type and rank $geq 2$, thereby providing a unified” proof of expansion in these groups.

Detailed Information

Author:Mikhail Ershov
Publication Year:2017
ISBN:9781470426040
Pages:148
Language:English
File Size:1.2
Format:PDF
Price:FREE
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