Cohomological Equation on the Discrete Heisenberg Group

TL;DR

This paper investigates the cohomological equations on the discrete Heisenberg group, providing conditions for solutions within the context of discrete dynamical systems on this mathematical structure.

Contribution

It offers new criteria for solving cohomological equations specifically on the discrete Heisenberg group, advancing understanding of dynamical systems in this setting.

Findings

Established conditions for solutions to cohomological equations on the discrete Heisenberg group

Enhanced understanding of discrete dynamical systems on non-abelian groups

Contributed to the mathematical theory of cohomology in group dynamics

Abstract

Let $\h_1$ be the one-dimensional Heisenberg group. In this paper, we consider some aspects of discrete dynamical systems on $\h_1$ and give a condition for the solution of a cohomological equations on the group.