GTA Seminar in Week 3 -- Wednesday, 13 August, 11:00-12:00 in Carslaw 535A
Speaker: Peter Abramenko (Virginia)
Title: On finite and elementary generation of \(SL_2(R)\)
Abstract: Let \(R\) be an integral domain which is finitely generated as a ring.
Interesting questions regarding \(SL_2(R)\) are whether this group is finitely generated
or whether it is generated by elementary matrices. I will explain how these two
questions are related, and present a brief survey of some well-known results in this
context.
The main part of the talk will be devoted to the following (new) Theorem: Let
\(R_0\) be a finitely generated integral domain of Krull dimension greater than 1 (e.g.
\(R_0 = Z[x]\) or \(F_q[x,y]),\) \(R = R_0[t]\) the polynomial ring over \(R_0\) and
\(F\) the field of fractions of \(R.\) Then *no* subgroup of \(SL_2(F)\) containing
\(SL_2(R)\) is finitely generated.
I will also explain why the action of \(SL_2(F)\) on
an appropriate (Bruhat-Tits) tree is an important ingredient of the proof of this
theorem.
Please join us for lunch after the talk!
Calendar
(ICS file) download, for import into your favourite calendar application
UNCLUTTER
for printing
AUTHENTICATE to mark the scnews item as read