- search hit 1 of 1
On central extensions of SL(2, F) admitting left-orderings
- 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.
| Author details: | Hans H. Brungs, Joachim GräterGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.jalgebra.2017.05.025 |
| ISSN: | 0021-8693 |
| ISSN: | 1090-266X |
| Title of parent work (English): | Journal of Algebra |
| Publisher: | Elsevier |
| Place of publishing: | San Diego |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/06/06 |
| Publication year: | 2017 |
| Release date: | 2022/01/12 |
| Tag: | Central extensions of groups; Euclidean fields; Left-ordered groups; Order-preserving bijections; Ordered fields; Perfect groups; Universal covering group |
| Volume: | 486 |
| Number of pages: | 40 |
| First page: | 288 |
| Last Page: | 327 |
| Funding institution: | NSERC; DFG |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
