Non-commutative geometry and covariance: from the quantum plane to the quantum tensors

TL;DR

This paper explores the mathematical structure of quantum tensors and their covariance properties using non-commutative geometry and the R-matrix formalism, focusing on the quantum plane and quantum tensors.

Contribution

It derives reflection and braid equations for rank two q-tensors based on covariance properties, advancing the understanding of quantum vector spaces.

Findings

Derived reflection equations for quantum tensors

Established braid relations from covariance principles

Connected non-commutative geometry with quantum tensor algebra

Abstract

Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.