On the structure of inhomogeneous quantum groups

TL;DR

This paper studies the structure of inhomogeneous quantum groups, focusing on their algebraic relations, R-matrices, and geometric analogues, with applications to quantum Poincare groups.

Contribution

It provides a detailed analysis of inhomogeneous quantum groups, establishing conditions for their proper size and deriving their R-matrices and Minkowski space analogues.

Findings

Established conditions for the correct size of inhomogeneous quantum groups

Derived R-matrices for these quantum groups

Constructed analogues of Minkowski space for the groups

Abstract

We investigate inhomogeneous quantum groups G built from a quantum group H and translations. The corresponding commutation relations contain inhomogeneous terms. Under certain conditions (which are satisfied in our study of quantum Poincare groups [12]) we prove that our construction has correct `size', find the R-matrices and the analogues of Minkowski space for G.