Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wild

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

Wild problems

Classification

Associative algebras

Lie algebras

Metabelian groups

Mathematics

matematik

Publication and Content Type

ref (subject category)

art (subject category)