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Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wild
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
Faculty of Mechanics and Mathematics, Kiev National Taras Shevchenko University, Kiev, Ukraine.ORCID iD: 0000-0001-9110-6182
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
Institute of Mathematics, Kiev, Ukraine.
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 $p^{3}$ 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
Mathematics
##### Identifiers
OAI: oai:DiVA.org:oru-74873DiVA, id: diva2:1332914
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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#### Authority records BETA

Dmytryshyn, Andrii

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Dmytryshyn, Andrii
##### In the same journal
The Electronic Journal of Linear Algebra
##### On the subject
Algebra and Logic

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Cite
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