Quantum Lorentz Group Having Gauss Decomposition Property

Abstract

A new deformation of $SL(2,\mathbf{C})$ (considered as a real Lie group) is constructed and shown to have a Gauss type decomposition. The groups entering this decomposition are identified as $E_{\mu }(2)$ and its Pontryagin dual ${\hat{E}}_{\mu }(2)$. The whole group is the double group built over $E_{\mu }(2)$.