Abstract
For an arbitrary euclidean field F we introduce a central extension (G(F),Φ) of SL(2,F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order-preserving bijections of the convex hull of Q in F. If F=R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2,R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.