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SUMMARY:Waldemar Hołubowski (Silesian University of Technology)
DTSTART:20210607T063000Z
DTEND:20210607T073000Z
DTSTAMP:20260423T053135Z
UID:SiN/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/22/">Nor
 mal subgroups in the group of column-finite infinite matrices</a>\nby Wald
 emar Hołubowski (Silesian University of Technology) as part of Symmetry i
 n Newcastle\n\n\nAbstract\nThe classical result\, due to Jordan\, Burnside
 \, Dickson\, says that every normal subgroup of $GL(n\, K)$ ($K$ - a field
 \, $n \\geq 3$) 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 c
 enter and the group of linear transformations $g$ such that $g-id_V$ has f
 inite dimensional range the proof is not complete. We fill this gap for co
 untably dimensional $V$ giving description of the lattice of normal subgro
 ups in the group of infinite column-finite matrices indexed by positive in
 tegers over any field. Similar results for Lie algebras of matrices will b
 e surveyed.\n\nThe talks is based on results presented in https://arxiv.or
 g/abs/1808.06873 and https://arxiv.org/abs/1806.01099.\n\n(joint work with
  Martyna Maciaszczyk and Sebastian Zurek.)\n
LOCATION:https://researchseminars.org/talk/SiN/22/
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