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

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

2007-09-16

arxiv.org/abs/0709.2463v1

Linear Algebra Appl. 407 (2005) 249-262

Mathematics

Representation Theory

18 pages

Scientific paper

10.1016/j.laa.2005.05.007

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.

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