Property ($T$) for Groups Graded by Root Systems Paperback / softback
by Mikhail Ershov, Andrei Jaikin-Zapirain, Martin Kassabov
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
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 ${\mathrm St}_{\Phi}(R)$ and the elementary Chevalley group $\mathbb E_{\Phi}(R)$ 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.
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Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:135 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2017
- Category:
- ISBN:9781470426040
Other Formats
- PDF from £67.50
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:135 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2017
- Category:
- ISBN:9781470426040
