Pseudo-Riemannian metrics on bicovariant bimodules

TL;DR

This paper investigates pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras, establishing a correspondence between metrics on bimodules and their cocycle deformations, thus advancing the understanding of geometric structures in quantum algebra.

Contribution

It demonstrates a one-to-one correspondence between pseudo-Riemannian invariant metrics on bicovariant bimodules and their cocycle deformations, clarifying their properties.

Findings

Metrics on bimodules and deformations correspond uniquely.

Properties of pseudo-Riemannian invariant metrics are clarified.

The study enhances understanding of geometric structures in quantum algebra.

Abstract

We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a bicovariant bimodule and its cocycle deformations are in one to one correspondence.