On symmetries of 3-dimensional algebraic continued fractions

I. A. Tlyustangelov<sup>ab

a</sup> Lomonosov Moscow State University (Moscow)
^b Moscow Center of Fundamental and Applied Mathematics (Moscow)

Abstract: In this paper we prove in detail a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension 4. We also present a new proof of the criterion for an algebraic continued fraction to have a proper cyclic palindromic symmetry in dimension 4. As a multidimensional generalization of continued fractions, we consider Klein polyhedra.

Keywords: Klein polyhedra, algebraic lattices.

UDC: 511.48

Received: 14.09.2022
Accepted: 24.04.2023

DOI: 10.22405/2226-8383-2023-24-1-139-181