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

Genrich Belitskii, Ruvim Lipyanski, Vladimir V. Sergeichuk

Published 2007-09-16Version 1

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.