02942nam 2200565 450 991048093980332120170822144404.01-4704-0339-0(CKB)3360000000464930(EBL)3114354(SSID)ssj0000973914(PQKBManifestationID)11553858(PQKBTitleCode)TC0000973914(PQKBWorkID)10984656(PQKB)10409329(MiAaPQ)EBC3114354(PPN)195416325(EXLCZ)99336000000046493020020117d2002 uy| 0engur|n|---|||||txtccrSome generalized Kac-Moody algebras with known root multiplicities /Peter NiemannProvidence, Rhode Island :American Mathematical Society,2002.1 online resource (137 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 746"Volume 157, number 746 (second of 5 numbers)."0-8218-2888-6 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;no. 746.Kac-Moody algebrasRoot systems (Algebra)Electronic books.Kac-Moody algebras.Root systems (Algebra)510 s512/.55Niemann Peter1965-992767MiAaPQMiAaPQMiAaPQBOOK9910480939803321Some generalized Kac-Moody algebras with known root multiplicities2273273UNINA