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SUMMARY:Symmetry in Newcastle\, Monday 7th June 2021
DESCRIPTION:Symmetry in Newcastle seminar is here again! \nThe confirmed speakers for next Monday are Waldemar Hołubowski\, Silesian University of Technology.\nFeel free to grab a beverage appropriate for your respective timezone and join us for a friendly chat after the talk! \nThe 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 \nDate: 7 June 2021 Time: 16:30–17:30 AEST (06:30–07:30 UTC)\nSpeaker: Waldemar Hołubowski\nTitle: Normal subgroups in the group of column-finite infinite matrices \nAbstract: 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-idV 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. \nThis is based on results presented in https://arxiv.org/abs/1808.06873 and https://arxiv.org/abs/1806.01099. \n(joint work with Martyna Maciaszczyk and Sebastian Zurek.) \n \nThe zoom link is https://uonewcastle.zoom.us/j/82596235512. \n \nHope to see some of you on Monday! \nMichal
URL:https://austms.org.au/event/symmetry-in-newcastle-monday-7th-june-2021/
CATEGORIES:Symmetry in Newcastle
ORGANIZER;CN="Michal%20Ferov":MAILTO:michal.ferov@newcastle.edu.au
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