Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wild
2009 (English)In: The Electronic Journal of Linear Algebra, ISSN 1081-3810, Vol. 18, 516-529 p.Article in journal (Refereed) Published
Let F be a field of characteristic different from 2. It is shown that the problems of classifying
(i) local commutative associative algebras over F with zero cube radical,
(ii) Lie algebras over F with central commutator subalgebra of dimension 3, and
(iii) finite p-groups of exponent p with central commutator subgroup of order are hopeless since each of them contains
• the problem of classifying symmetric bilinear mappings UxU → V , or
• the problem of classifying skew-symmetric bilinear mappings UxU → V ,
in which U and V are vector spaces over F (consisting of p elements for p-groups (iii)) and V is 3-dimensional. The latter two problems are hopeless since they are wild; i.e., each of them contains the problem of classifying pairs of matrices over F up to similarity.
Place, publisher, year, edition, pages
2009. Vol. 18, 516-529 p.
Wild problems, Classification, Associative algebras, Lie algebras, Metabelian groups
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-88008OAI: oai:DiVA.org:umu-88008DiVA: diva2:713114