Buch, Englisch, Band 5, 278 Seiten, Previously published in hardcover, Format (B × H): 160 mm x 240 mm, Gewicht: 477 g
Reihe: Algebra and Applications
Buch, Englisch, Band 5, 278 Seiten, Previously published in hardcover, Format (B × H): 160 mm x 240 mm, Gewicht: 477 g
Reihe: Algebra and Applications
ISBN: 978-90-481-7254-2
Verlag: Springer Netherlands
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Borcherds-Kac-Moody Lie Superalgebras.- Singular Theta Transforms of Vector Valued Modular Forms.- ?-Graded Vertex Algebras.- Lorentzian BKM Algebras.
