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

2005/07/15 by Genrich Belitskii, Ruvim Lipyanski, Vladimir V. Sergeichuk · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT #msc:15A21 #msc:16G60 #msc:17B30

paper · pdf · doi:10.1016/j.laa.2005.05.007

published as Linear Algebra Appl. 407 (2005) 249-262 · 18 pages

openalex publication_date 2005/07/15 · arxiv created 2007/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• The problems of classifying pairs of forms and local algebras with zero cube radical are wild
• Complexity of matrix problems

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