Property ($T$) for Groups Graded by Root Systems

Property ($T$) for Groups Graded by Root Systems
Author :
Publisher : American Mathematical Soc.
Total Pages : 148
Release :
ISBN-10 : 9781470426040
ISBN-13 : 1470426048
Rating : 4/5 (048 Downloads)

Book Synopsis Property ($T$) for Groups Graded by Root Systems by : Mikhail Ershov

Download or read book Property ($T$) for Groups Graded by Root Systems written by Mikhail Ershov and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.


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