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Property ($T$) for Groups Graded by Root Systems
Mikhail Ershov
Andrei Jaikin-Zapirain
Martin Kassabov
出版
American Mathematical Soc.
, 2017-09-25
主題
Mathematics / Algebra / General
Mathematics / Geometry / Algebraic
ISBN
1470426048
9781470426040
URL
http://books.google.com.hk/books?id=QJc3DwAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
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.