The problems of classifying pairs of forms and local algebras with zero cube radical are wild
Representation Theory
2007-09-18 v1
Abstract
We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of bilinear forms in which the second is symmetric (skew-symmetric), and local algebras with zero cube radical and square radical of dimension 2 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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Cite
@article{arxiv.0709.2460,
title = {The problems of classifying pairs of forms and local algebras with zero cube radical are wild},
author = {Genrich Belitskii and Vitalij M. Bondarenko and Ruvim Lipyanski and Vladimir V. Plachotnik and Vladimir V. Sergeichuk},
journal= {arXiv preprint arXiv:0709.2460},
year = {2007}
}
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10 pages