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

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

$200.00
$200.00
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Property ($T$) for Groups Graded by Root Systems
  • Property ($T$) for Groups Graded by Root Systems
  • Property ($T$) for Groups Graded by Root Systems
Property ($T$) for Groups Graded by Root Systems

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

$200.00
$200.00

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.

  • Author: Mikhail Ershov, Andrei Jaikin-Zapirain, Martin Kassabov
  • Publisher: American Mathematical Soc.
  • Published: 2017-09-25
  • Pages: 148

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