Symmetry in Newcastle, Monday 7th June 2021

Symmetry in Newcastle seminar is here again!

The confirmed speakers for next Monday are Waldemar Hołubowski, Silesian University of Technology.
Feel free to grab a beverage appropriate for your respective timezone and join us for a friendly chat after the talk!

The talks will be recorded and made available on our YouTube channel https://tinyurl.com/zerodimensionalgroup and our website https://zerodimensional.group/. The running time of the talk, title and abstract are as follows

Date: 7 June 2021       Time: 16:30–17:30 AEST (06:30–07:30  UTC)
Speaker: Waldemar Hołubowski
Title: Normal subgroups in the group of column-finite infinite matrices

Abstract: The classical result, due to Jordan, Burnside, Dickson, says that every normal subgroup of GL(n, K) (K – a field, n ≥ 3) which is not contained in the center, contains SL(n, K). A.Rosenberg gave description of normal subgroups of GL(V), where V is a vector space of any infinite cardinality dimension over a division ring. However, when he considers subgroups of the direct product of the center and the group of linear transformations g such that g-id_V has finite dimensional range the proof is not complete. We fill this gap for countably dimensional V giving description of the lattice of normal subgroups in the group of infinite column-finite matrices indexed by positive integers over any field. Similar results for Lie algebras of matrices will be surveyed.

This is based on results presented in https://arxiv.org/abs/1808.06873 and https://arxiv.org/abs/1806.01099.

(joint work with Martyna Maciaszczyk and Sebastian Zurek.)

 

The zoom link is https://uonewcastle.zoom.us/j/82596235512.

 

Hope to see some of you on Monday!

Michal