Normal subgroups in the group of column-finite infinite matrices

Waldemar HoĊ‚ubowski (Silesian University of Technology)

07-Jun-2021, 06:30-07:30 (3 years ago)

Abstract: The 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 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.

The talks is based on results presented in arxiv.org/abs/1808.06873 and arxiv.org/abs/1806.01099.

(joint work with Martyna Maciaszczyk and Sebastian Zurek.)

group theory

Audience: researchers in the discipline


Symmetry in Newcastle

Organizer: Michal Ferov*
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