umu.sePublications
Change search

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
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.
2009 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 18, p. 516-529Article 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
##### Keywords [en]
Wild problems, Classification, Associative algebras, Lie algebras, Metabelian groups
Mathematics
Mathematics
##### Identifiers
OAI: oai:DiVA.org:umu-88008DiVA, id: diva2:713114
Available from: 2014-04-21 Created: 2014-04-21 Last updated: 2018-06-08

#### Open Access in DiVA

No full text in DiVA

#### Authority records BETA

Dmytryshyn, Andrii

#### Search in DiVA

##### By author/editor
Dmytryshyn, Andrii
##### By organisation
Department of Computing Science
##### In the same journal
The Electronic Journal of Linear Algebra
Mathematics

urn-nbn

#### Altmetric score

urn-nbn
Total: 301 hits

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf