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RT Book, Whole SR Electronic DC OPAC T1 Automorphic Forms and Lie Superalgebras / by Urmie Ray T2 Algebra and Applications A1 Ray, Urmie A1 SpringerLink (Online service) YR 2006 FD 2006 SP X, 278 p K1 Mathematics K1 Nonassociative rings K1 Rings (Algebra) K1 Number theory K1 Mathematics K1 Non-associative Rings and Algebras K1 Number Theory PB Springer Netherlands PP Dordrecht SN 9781402050107 LA English (英語) CL DC23:512.48 NO A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice; and has an associated automorphic form having a product expansion describing its structure. Lie superalgebras are generalizations of Lie algebras, useful for depicting supersymmetry – the symmetry relating fermions and bosons. Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26. The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course. The necessary background is given within chapters or in appendices NO 書誌ID=1003001392; LK [E Book]http://dx.doi.org/10.1007/978-1-4020-5010-7 OL 30