TY  - JOUR
A1  - Brungs, Hans H.
A1  - Gräter, Joachim
T1  - On central extensions of SL(2, F) admitting left-orderings
JF  - Journal of Algebra
N2  - For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) 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.
KW  - Universal covering group
KW  - Central extensions of groups
KW  - Perfect groups
KW  - Ordered fields
KW  - Left-ordered groups
KW  - Order-preserving bijections
KW  - Euclidean fields
Y1  - 2017
U6  - https://doi.org/10.1016/j.jalgebra.2017.05.025
SN  - 0021-8693
SN  - 1090-266X
VL  - 486
SP  - 288
EP  - 327
PB  - Elsevier
CY  - San Diego
ER  -