TY - JOUR
T1 - Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild
AU - Belitskii, Genrich
AU - Lipyanski, Ruvim
AU - Sergeichuk, Vladimir V.
N1 - Funding Information:
∗ Corresponding author. E-mail addresses: [email protected] (G. Belitskii); [email protected] (R. Lipyanski); [email protected] (V.V. Sergeichuk). 1 Partially supported by Israel Science Foundation, Grant 186/01. 2 The research was started while this author was visiting the Ben-Gurion University of the Negev.
PY - 2005/9/15
Y1 - 2005/9/15
N2 - We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 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 the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity.
KW - Bilinear forms
KW - Nilpotent Lie algebras
KW - Wild problems
UR - http://www.scopus.com/inward/record.url?scp=24044475539&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2005.05.007
DO - 10.1016/j.laa.2005.05.007
M3 - Article
AN - SCOPUS:24044475539
SN - 0024-3795
VL - 407
SP - 249
EP - 262
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -