TY - BOOK
AU - Ray,Urmie
ED - SpringerLink (Online service)
TI - Automorphic Forms and Lie Superalgebras
T2 - Algebra and Applications
SN - 9781402050107
AV - QA252-252.5
U1 - 512.48 23
PY - 2006///
CY - Dordrecht
PB - Springer Netherlands
KW - Mathematics
KW - Nonassociative rings
KW - Rings (Algebra)
KW - Number theory
KW - Non-associative Rings and Algebras
KW - Number Theory
N1 - Borcherds-Kac-Moody Lie Superalgebras -- Singular Theta Transforms of Vector Valued Modular Forms -- ?-Graded Vertex Algebras -- Lorentzian BKM Algebras
N2 - 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
UR - http://dx.doi.org/10.1007/978-1-4020-5010-7
ER -