# The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 3, page 291-300
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topAbanina, L., and Mishchenko, S.. "The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0." Serdica Mathematical Journal 29.3 (2003): 291-300. <http://eudml.org/doc/219538>.

@article{Abanina2003,

abstract = {2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99,
17B01, 17B30, 20C30Let 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
and Young
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.This project was partially supported by RFBR, grants 01-01-00728, 02-01-00219 and
UR 04.01.036.},

author = {Abanina, L., Mishchenko, S.},

journal = {Serdica Mathematical Journal},

keywords = {Leibniz Algebras with Polynomial Identities; Varieties of Leibniz Algebras; Colength; Multiplicities; Codimensions; Leibniz algebras with polynomial identities; varieties of Leibniz algebras; codimensions; colength; multiplicities},

language = {eng},

number = {3},

pages = {291-300},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0},

url = {http://eudml.org/doc/219538},

volume = {29},

year = {2003},

}

TY - JOUR

AU - Abanina, L.

AU - Mishchenko, S.

TI - The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

JO - Serdica Mathematical Journal

PY - 2003

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 29

IS - 3

SP - 291

EP - 300

AB - 2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99,
17B01, 17B30, 20C30Let 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
and Young
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.This project was partially supported by RFBR, grants 01-01-00728, 02-01-00219 and
UR 04.01.036.

LA - eng

KW - Leibniz Algebras with Polynomial Identities; Varieties of Leibniz Algebras; Colength; Multiplicities; Codimensions; Leibniz algebras with polynomial identities; varieties of Leibniz algebras; codimensions; colength; multiplicities

UR - http://eudml.org/doc/219538

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.