Minimal Polynomials of Generalized Heisenberg Groups

TL;DR

This paper computes the minimal polynomials for generalized Heisenberg groups with canonical metrics to provide explicit examples of homogeneous Riemannian C_0-spaces.

Contribution

It offers explicit minimal polynomial calculations for generalized Heisenberg groups, enriching the understanding of their geometric properties.

Findings

Explicit minimal polynomials for generalized Heisenberg groups

Enhanced examples of homogeneous Riemannian C_0-spaces

Clarified the structure of these groups' minimal polynomials

Abstract

Every homogeneous Riemannian C_0-space (N,g) is associated with its minimal polynomial. To provide explicit examples, we compute the minimal polynomials for generalized Heisenberg groups equipped with their canonical left-invariant metrics.