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

Author(s)

Futorny, Vyacheslav ^[1] ; Klymchuk, Tetiana ^{[2, 3]} ; Petravchuk, Anatolii P. ^[3] ; Sergeichuk, Vladimir V. ^[4]

Affiliation

^[1] Univ Sao Paulo, Dept Math, Sao Paulo - Brazil

^[2] Univ Politecn Cataluna, Barcelona - Spain

^[3] Taras Shevchenko Univ, Fac Mech & Math, Kiev - Ukraine

^[4] Inst Math, Tereshchenkivska 3, Kiev - Ukraine

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 536, p. 201-209, JAN 1 2018.
• Web of Science Citations: 1

Abstract

For each two-dimensional vector space V of commuting n x n matrices over a field IF with at least 3 elements, we denote by V the vector space of all (n + 1) x (n + 1) matrices of the form {[}A 0 {*} 0] with A is an element of V. We prove the wildness of o the problem of classifying Lie algebras (V) over tilde 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. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/05864-9 - Classification problems in linear algebra and system theory
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International