Abstract
The chapter discusses star-closed sets of lines at 60° and 90°, leading to a theorem that leaves only a restricted number of possibilities, of a specific structure. These possibilities are realized by the root systems An, Dn, E8, E7, E6 defined in terms of lines. The chapter discusses the relations to the official Root Systems, as they occur in geometry and algebra. The chapter also discusses the graphs represented by subsets of the root systems: line graphs of complete bipartite graphs for An, Hoffman's generalized line graphs for Dn, and various exceptional graphs for E8. The chapter also presents the application to Hadamard matrices.
Sign-in/Register to access full text options 
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 callDisclaimer: 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.
