The problems of classifying pairs of forms and local algebras with zero cube radical are wild

Details The problems of classifying pairs of forms and local algebras with zero cube radical are wild The problems of classifying pairs of forms and local algebras with zero cube radical are wild

2007-09-16

arxiv.org/abs/0709.2460v1

Linear Algebra Appl. 402 (2005) 135-142

Mathematics

Representation Theory

10 pages

Scientific paper

10.1016/j.laa.2004.12.016

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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