Conservative algebras of 2-dimensional algebras, V.

Abstract

The notion of conservative algebras appeared in a pa- per of Kantor in 1972. Later, he de ned the conservative algebra W (n) of all algebras (i.e., bilinear maps) on the n-dimensional vec- tor space. If n > 1, then the algebra W (n) does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). It looks like that W (n) in the theory of con- servative algebras plays a similar role with the role of gln in the theory of Lie algebras. Namely, an arbitrary conservative algebra can be obtained from a universal algebra W (n) for some n ∈ N. The present paper is a part of a series of papers, which dedicated to the study of the algebra W (2) and its principal subalgebras.