Geodesic
On identities of model algebras
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1210-1226

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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.
Keywords: Lie nilpotent algebra, model algebra, identity in two variables
Mots-clés : algebra kernel. 
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     title = {On identities of model algebras},
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S. V. Pchelintsev. On identities of model algebras. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1210-1226. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a4/