Some Generalized Kac-Moody Algebras with Known Root Multiplicities.

Intro -- Contents -- Introduction -- Chapter 1. Generalized Kac-Moody Algebras -- 1.1. Definition and Fundamental Properties -- 1.2. The Denominator Formula -- 1.3. Vertex Algebras -- 1.4. The Fake Monster Lie Algebra -- 1.5. The Twisted Denominator Formula -- 1.6. Construction of the GKMs -- 1.7. Root Multiplicities -- Chapter 2. Modular Forms -- 2.1. Review of Modular Group and Modular Forms -- 2.2. Some Modular Forms Related to Eta -- Chapter 3. Lattices and their Theta-Functions -- 3.1. Review of Results about Lattices -- 3.2. The Character of Theta -- Chapter 4. The Proof of Theorem 1.7 -- 4.1. The Theta-Function of L* -- 4.2. Sums of Quadratic Residues -- 4.3. The Short Vectors of L* -- 4.4. The Conclusion of the Proof -- Chapter 5. The Real Simple Roots -- 5.1. The Set of Real Simple Roots -- 5.2. Holes and Dynkin Diagrams -- 5.3. The Volume Formula -- 5.4. The Automorphism Groups -- Chapter 6. Hyperbolic Lie Algebras -- 6.1. Wan's classification -- 6.2. Finite, Affine, and Hyperbolic Subalgebras -- 6.3. Conclusions -- Appendix A -- N=23 -- N=11 -- N=7 -- N=5 -- N=3 -- N=2 -- Appendix B -- Bibliography -- Notation.

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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.