02735nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001600169072002300185082001500208100002500223245008400248264004600332300003200378336002600410337002600436338003600462347002400498490003400522505015800556520125600714650001701970650002601987650002102013650001902034650001702053650004002070650001902110710003402129773002002163776003602183830003402219856004802253978-1-4020-5010-7DE-He21320180115171450.0cr nn 008mamaa100301s2006 ne | s |||| 0|eng d a97814020501077 a10.1007/978-1-4020-5010-72doi 4aQA252-252.5 7aPBF2bicssc 7aMAT0020102bisacsh04a512.482231 aRay, Urmie.eauthor.10aAutomorphic Forms and Lie Superalgebrash[electronic resource] /cby Urmie Ray. 1aDordrecht :bSpringer Netherlands,c2006. aX, 278 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgebra and Applications ;v50 aBorcherds-Kac-Moody Lie Superalgebras -- Singular Theta Transforms of Vector Valued Modular Forms -- ?-Graded Vertex Algebras -- Lorentzian BKM Algebras. aA 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. 0aMathematics. 0aNonassociative rings. 0aRings (Algebra). 0aNumber theory.14aMathematics.24aNon-associative Rings and Algebras.24aNumber Theory.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781402050091 0aAlgebra and Applications ;v540uhttp://dx.doi.org/10.1007/978-1-4020-5010-7