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

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10.1016/j.laa.2017.09.019
 
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hdl:2117/108725

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Futorny, Vyacheslav
Klymchuk, TetianaMés informació
Petravchukc, Anatolii P.
Sergeichuk, Vladimir V.
Document typeArticle
Defense date2018-01-01
PublisherElsevier
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
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.
CitationFutorny, V. [et al.]. Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras. "Linear algebra and its applications", 1 Gener 2018, vol. 536, p. 201-209. 
URIhttp://hdl.handle.net/2117/108725
DOI10.1016/j.laa.2017.09.019
ISSN0024-3795
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S0024379517305438
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