Affiliation:
1. Financial University under the Government of the Russian Federation, Moscow
2. Saint Petersburg State University
Abstract
A sharp upper bound for the nilpotency index of the commutator ideal
of a $2$-generated subalgebra of an arbitrary model algebra is given;
this estimate is about half that for arbitrary
Lie nilpotent algebras of the same class. All identities in two variables
that hold in the model algebra of multiplicity $3$ are found. For any
$m\geqslant 3$, in a free Lie nilpotent algebra $F^{(2m+1)}$ of class $2m$,
the kernel polynomial of smallest possible degree is indicated.
It is proved that the degree of any identity of a model algebra is greater
than its multiplicity.
Funder
Russian Science Foundation
Publisher
Steklov Mathematical Institute