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Most common price: £67 (59 days, 100.0%)

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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.

Product Specifications

Format: paperback
ASIN: 1470426048
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 October 2017
Listed Since: 28 June 2017

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

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

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