Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild

Genrich Belitskii; Ruvim Lipyanski; Vladimir V. Sergeichuk

doi:10.1016/j.laa.2005.05.007

Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild

Genrich Belitskii, Ruvim Lipyanski, Vladimir V. Sergeichuk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

Original language	English
Pages (from-to)	249-262
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	407
Issue number	1-3
DOIs	https://doi.org/10.1016/j.laa.2005.05.007
State	Published - 15 Sep 2005

Keywords

Bilinear forms
Nilpotent Lie algebras
Wild problems

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2005.05.007

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title = "Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild",

abstract = "We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.",

keywords = "Bilinear forms, Nilpotent Lie algebras, Wild problems",

author = "Genrich Belitskii and Ruvim Lipyanski and Sergeichuk, {Vladimir V.}",

note = "Funding Information: ∗ Corresponding author. E-mail addresses: genrich@cs.bgu.ac.il (G. Belitskii); lipyansk@cs.bgu.ac.il (R. Lipyanski); sergeich@imath.kiev.ua (V.V. Sergeichuk). 1 Partially supported by Israel Science Foundation, Grant 186/01. 2 The research was started while this author was visiting the Ben-Gurion University of the Negev.",

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doi = "10.1016/j.laa.2005.05.007",

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T1 - Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild

AU - Belitskii, Genrich

AU - Lipyanski, Ruvim

AU - Sergeichuk, Vladimir V.

N1 - Funding Information: ∗ Corresponding author. E-mail addresses: genrich@cs.bgu.ac.il (G. Belitskii); lipyansk@cs.bgu.ac.il (R. Lipyanski); sergeich@imath.kiev.ua (V.V. Sergeichuk). 1 Partially supported by Israel Science Foundation, Grant 186/01. 2 The research was started while this author was visiting the Ben-Gurion University of the Negev.

PY - 2005/9/15

Y1 - 2005/9/15

N2 - We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

AB - We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

KW - Bilinear forms

KW - Nilpotent Lie algebras

KW - Wild problems

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DO - 10.1016/j.laa.2005.05.007

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SN - 0024-3795

VL - 407

SP - 249

EP - 262

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild

Abstract

Keywords

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