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

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.

18 pages

References in corpus (3)

• Classification problems for system of forms and linear mappings
• Complexity of matrix problems
• The problems of classifying pairs of forms and local algebras with zero cube radical are wild

Cited by in corpus (5)

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• Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras
• Congruence of matrix spaces, matrix tuples, and multilinear maps
• The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence
• Classification of a Class of Solvable Real Lie Algebras by using Techniques in Matrix Theory