## Topology & Geometric Group Theory Seminar

## Fall 2010

### 1:30 – 2:30, Malott 253

Tuesday, November 9

**
Matt Zaremsky**, University of Virginia

*Weyl transitive but not strongly transitive group actions on
buildings*

In recent work with Peter Abramenko, we have exhibited two large
classes of group actions on buildings that are Weyl transitive but not
strongly transitive with respect to any apartment system. The first
class of examples arises by inspecting torsion properties in Chevalley
groups. The other, more recent results involve analyzing division
algebras, with the conclusion that for any central F-division algebra
D of degree greater than 2, the action of the norm-1 or multiplicative
group on the associated building is "not even close" to being strongly
transitive. For certain fields F, we can exhibit such actions that
are nonetheless Weyl transitive.

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