Locally Finite Root Systems.

Intro -- Contents -- Introduction -- 1. The category of sets in vector spaces -- 2. Finiteness conditions and bases -- 3. Locally finite root systems -- 4. Invariant inner products and the coroot system -- 5. Weyl groups -- 6. Integral bases, root bases and Dynkin diagrams -- 7. Weights and coweights -- 8. Classification -- 9. More on Weyl groups and automorphism groups -- 10. Parabolic subsets and positive systems for symmetric sets in vector spaces -- 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group -- 12. Closed and full subsystems of finite and infinite classical root systems -- 13. Parabolic subsets of root systems: classification -- 14. Positive systems in root systems -- 15. Positive linear forms and facets -- 16. Dominant and fundamental weights -- 17. Gradings of root systems -- 18. Elementary relations and graphs in 3-graded root systems -- Appendix A. Some standard results on finite root systems -- Appendix B. Cones defined by totally preordered sets -- Bibliography -- Index of notations -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- W -- Z.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.