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

Genrich Belitskii, Ruvim Lipyanski, Vladimir V. Sergeichuk

Research output: Contribution to journalArticlepeer-review

17 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 languageEnglish
Pages (from-to)249-262
Number of pages14
JournalLinear Algebra and Its Applications
Volume407
Issue number1-3
DOIs
StatePublished - 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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