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Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras

Author
Futorny, V.; Klymchuk, T.; Petravchukc, A.; Sergeichuk , V.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2018-01-01
Volume
536
First page
201
Last page
209
DOI
https://doi.org/10.1016/j.laa.2017.09.019 Open in new window
Repository
http://hdl.handle.net/2117/108725 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0024379517305438 Open in new window
Abstract
For each two-dimensional vector space V of commuting n×n matrices over a field F with at least 3 elements, we denote by V˜ the vector space of all (n+1)×(n+1) matrices of the form [A¿00] with A¿V. We prove the wildness of the problem of classifying Lie algebras V˜ with the bracket operation [u,v]:=uv-vu. We also prove the wildness of the problem of classifying two-dimensional vector spaces consisting of commuting linear operators on a vector space over a field.
Keywords
Matrix Lie algebras, Spaces of commuting linear operators, Wild problems
Group of research
SCL-EG - Linear Control Systems: a Geometric Approach

Participants

  • Futorny, Vyacheslav  (author)
  • Klymchuk, Tetiana  (author)
  • Petravchukc, Anatolii P.  (author)
  • Sergeichuk, Vladimir V.  (author)

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