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

2005/02/02 by Genrich Belitskii, Vitalij M. Bondarenko, В. М. Бондаренко +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT #msc:15A21 #msc:16G60 #msc:17B30

paper · pdf · doi:10.1016/j.laa.2004.12.016

published as Linear Algebra Appl. 402 (2005) 135-142 · 10 pages

openalex publication_date 2005/02/02 · arxiv created 2007/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric), and local algebras with zero cube radical and square radical of dimension 2 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.

Citations

• Complexity of matrix problems

Cited by

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