Problems of classifying associative or lie algebras ver a field of characteristic not two and finite etabelian groups are wild

Genrich Belitskii, Andrii R. Dmytryshyn, Ruvim Lipyanski, Vladimir V. Sergeichuk, Arkady Tsurkov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 p3 are hopeless since each of them contains · the problem of classifying symmetric bilinear mappings U × U → V, or · the problem of classifying skew-symmetric bilinear mappings U × U → 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.

Original languageEnglish
Pages (from-to)516-529
Number of pages14
JournalElectronic Journal of Linear Algebra
Volume18
StatePublished - 1 Jan 2009

Keywords

  • Associative algebras
  • Classification
  • Lie algebras
  • Metabelian groups
  • Wild problems

ASJC Scopus subject areas

  • Algebra and Number Theory

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