On The Inhomogeneous Quantum Groups

TL;DR

This paper constructs multi-parametric quantum groups related to inhomogeneous linear groups using deformations of function algebras and universal enveloping algebras, advancing the understanding of quantum group structures.

Contribution

It introduces new multi-parametric quantum groups for inhomogeneous linear groups, expanding the algebraic framework of quantum group theory.

Findings

Construction of multi-parametric quantum groups $\IGLq{n}$ and $\Uq{\igl{n}}$

Extension of deformation techniques to inhomogeneous groups

Framework for further exploration of quantum symmetries

Abstract

Using the multi-parametric deformation of the algebra of functions on $ \GL{n+1} $ and the universal enveloping algebra $ \U{\igl{n+1}} $, we construct the multi-parametric quantum groups $ \IGLq{n} $ and $ \Uq{\igl{n}} $.