Abstract
Rank one groups were introduced by F. G. Timmesfeld as the building blocks of Lie type groups. Division pairs are algebraic objects categorically equivalent to Moufang sets. We define a functor $\varDelta$ from rank one groups to division pairs and prove that $\varDelta$ has a left adjoint $\varSigma$, given by a Steinberg type construction. We also extend the theory of the quasi-inverse and the Bergmann operators, well known from Jordan pairs, to this setting. As an application, we show that identities proved by T. De Medts and Y. Segev for Moufang sets hold in arbitrary rank one groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Bulletin of the Belgian Mathematical Society - Simon Stevin
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.
