Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wildShow others and affiliations
2009 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 18, p. 516-529, article id 41Article in journal (Refereed) Published
Abstract [en]
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, p. 516-529, article id 41
Keywords [en]
Wild problems, Classification, Associative algebras, Lie algebras, Metabelian groups
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-74873DOI: 10.13001/1081-3810.1329OAI: oai:DiVA.org:oru-74873DiVA, id: diva2:1332914
2019-06-282019-06-282019-09-20Bibliographically approved