A. A. Mikhalev, K. M. Shipilova, “Primitive elements of free Lie algebras over the field <nobr>${\mathbb F}_{3}$</nobr>”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2025, Number 3,Pages <nobr>80

Short notes

Primitive elements of free Lie algebras over the field ${\mathbb F}_{3}$

A. A. Mikhalev, K. M. Shipilova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The problem of finding primitive elements of degree two and three in the free Lie algebra of rank three over the field ${\mathbb F}_{3}$ is solved. Also estimates of the number of primitive elements of degree two with arbitrary number of generators over the field ${\mathbb F}_{3}$ are obtained.

Key words: free Lie algebra, primitive element, elementary automorphism, free differential calculus, primitiveness criterion.

UDC: 512.554

Received: 07.06.2024

DOI: 10.55959/MSU0579-9368-1-66-3-13