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101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aSome generalized Kac-Moody algebras with known root multiplicities /$fPeter Niemann
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2002.
215   $a1 online resource (137 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 746
300   $a"Volume 157, number 746 (second of 5 numbers)."
311   $a0-8218-2888-6 
320   $aIncludes bibliographical references.
327   $a""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""
327   $a""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""
327   $a""Bibliography""""Notation""
410  0$aMemoirs of the American Mathematical Society ;$vno. 746.
606   $aKac-Moody algebras
606   $aRoot systems (Algebra)
608   $aElectronic books.
615  0$aKac-Moody algebras.
615  0$aRoot systems (Algebra)
676   $a510 s
676   $a512/.55
700   $aNiemann$b Peter$f1965-$0992767
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910480939803321
996   $aSome generalized Kac-Moody algebras with known root multiplicities$92273273
997   $aUNINA