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: [email protected] (G. Belitskii), [email protected] (V.M. Bondarenko), [email protected] (R. Lipyanski), [email protected] (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
SN - 0024-3795
VL - 402
SP - 135
EP - 142
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -