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| QA564.SPR. FCT 94900 Algebraic geometry and number theory | QA177.SPR. FCT 94902 Classes of finite groups | QA334.SPR. FCT 94903 Intelligent algorithms in ambient and biomedical computing | QA252.3.SPR. FCT 94904 Automorphic forms and Lie superalgebras | QA300.SPR. FCT 94905 Conformal and potential analysis in Hele-Shaw cell | QA641.SPR. FCT 94908 Curve e superfici | QA274.42.SPR. FCT 94912 Case studies in spatial point process modeling |
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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.
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