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arXiv · 0709.2463

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

Genrich Belitskii·Ruvim Lipyanski·Vladimir V. Sergeichuk
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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.

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Genrich Belitskii, Ruvim Lipyanski, Vladimir V. Sergeichuk. 2007-09-16. Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild. https://doi.org/10.1016/j.laa.2005.05.007

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