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

Belitskii, Genrich; Lipyanski, Ruvim; Sergeichuk, Vladimir V.

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

Authors

Belitskii, Genrich

Lipyanski, Ruvim

Sergeichuk, Vladimir V.

Description

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.
18 pages