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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: | |
Price: | FREE |
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