Finite generatedness of Veronese subalgebras of a free alternative algebra of finite rank

S. V. Pchelintsev^a, I. P. Shestakov<sup>bcd

a</sup> Financial University under the Government of the Russian Federation, Moscow
^b Universidade de São Paulo, Instituto de Matemática e Estatística
^c SUSTech International Center for Mathematics, Southern University of Science and Technology
^d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: It is proved that, for any natural $n$, the subalgebra generated by words of length divisible by $n$ on generators (the Veronese $n$-subalgebra) in a free finitely generated alternative algebra is finitely generated.

Keywords: Veronese subalgebra, free alternative algebra of finite rank.

UDC: 512.554

Received: 23.11.2023
Revised: 04.12.2024

DOI: 10.33048/alglog.2024.63.106

 English version: Algebra and Logic, 2024, 63:1, 56–64