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Complexity of matrix problems
In representation theory, the problem of classifying pairs of matrices up to
simultaneous similarity is used as a measure of complexity; classification
problems containing it are called wild problems. We show in an explicit form
that this problem contains all classification matrix problems given by quivers
or posets. Then we prove that it does not contain (but is contained in) the
problem of classifying three-valent tensors. Hence, all wild classification
problems given by quivers or posets have the same complexity; moreover, a
solution of any one of these problems implies a solution of each of the others.
The problem of classifying three-valent tensors is more complicated.Comment: 24 page
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