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

Released on by Mikhail Ershov
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  • Property ($T$) for Groups Graded by Root Systems Book Detail

  • Author : Mikhail Ershov
  • Release Date : 2017-09-25
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 148
  • ISBN 13 : 1470426048
  • File Size : 3,3 MB
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Property ($T$) for Groups Graded by Root Systems by Mikhail Ershov PDF Summary

Book Description: 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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