£66.50

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

Algebra

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About the Author Mikhail Ershov, University of Virginia, Charlottesville, Virginia.Andrei Jaikin-Zapirain, Universidad Autonoma de Madrid, Spain and Instituto de Ciencias Matematicas, Madrid, Spain.Martin Kassabov, Cornell University, Ithaca, New York, and University of Southampton, United Kingdom. Product 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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