TY - JOUR

T1 - The problems of classifying pairs of forms and local algebras with zero cube radical are wild

AU - Belitskii, Genrich

AU - Bondarenko, Vitalij M.

AU - Lipyanski, Ruvim

AU - Plachotnik, Vladimir V.

AU - Sergeichuk, Vladimir V.

N1 - Funding Information:
E-mail addresses: genrich@cs.bgu.ac.il (G. Belitskii), vit-bond@imath.kiev.ua (V.M. Bondarenko), lipyansk@cs.bgu.ac.il (R. Lipyanski), sergeich@imath.kiev.ua (V.V. Sergeichuk). 1 Partially supported by Israel Science Foundation, Grant 186/01. 2 Partially supported by Ukrainian SFFR, Grant 01.07/00132.

PY - 2005/6/1

Y1 - 2005/6/1

N2 - 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.

AB - 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.

KW - Local algebras

KW - Pairs of bilinear forms

KW - Wild problems

UR - http://www.scopus.com/inward/record.url?scp=17744378164&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2004.12.016

DO - 10.1016/j.laa.2004.12.016

M3 - Article

AN - SCOPUS:17744378164

VL - 402

SP - 135

EP - 142

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -