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Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wild
Ben-Gurion University of the Negev, Israel.
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Ben-Gurion University of the Negev, Israel.
Institute of Mathematics, Kiev, Ukraine.
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2009 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 18, 516-529 p.Article 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, 516-529 p.
Keyword [en]
Wild problems, Classification, Associative algebras, Lie algebras, Metabelian groups
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-88008OAI: oai:DiVA.org:umu-88008DiVA: diva2:713114
Available from: 2014-04-21 Created: 2014-04-21 Last updated: 2017-12-05

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Dmytryshyn, Andrii

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