Leibniz Algebras with Polynomial Identities Varieties of Leibniz Algebras Colength Multiplicities Codimensions
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 29, No 3, (2003), 291p-300p
Let F be a field of characteristic zero. In this paper we study
the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0.
The algebras of this variety are left nilpotent of class not more than 3. We
give a complete description of the vector space of multilinear identities in
the language of representation theory of the symmetric group Sn
diagrams. We also show that the variety
3N is generated by an abelian
extension of the Heisenberg Lie algebra. It has turned out that
3N has many
properties which are similar to the properties of the variety of the abelian-by-nilpotent of class 2 Lie algebras. It has overexponential growth of the
codimension sequence and subexponential growth of the colength sequence.