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OverviewThe Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations. Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. The authors organize fundamental results in a unified way and refine existing proofs. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widely believed to be true, are collated, and results which are known but not verified are proven, such as the corrected structure theorem of Fock modules in chapter eight. This book will be of interest to a wide range of mathematicians and physicists from the level of graduate students to researchers. Full Product DetailsAuthor: Kenji Iohara , Yoshiyuki KogaPublisher: Springer London Ltd Imprint: Springer London Ltd Edition: 2011 ed. Dimensions: Width: 15.50cm , Height: 2.60cm , Length: 23.50cm Weight: 1.910kg ISBN: 9780857291592ISBN 10: 0857291599 Pages: 474 Publication Date: 25 November 2010 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsPreliminary.- Classification of Harish-Chandra Modules.- The Jantzen Filtration.- Determinant Formulae.- Verma Modules I: Preliminaries.- Verma Modules II: Structure Theorem.- A Duality among Verma Modules.- Fock Modules.- Rational Vertex Operator Algebras.- Coset Constructions for sl2.- Unitarisable Harish-Chandra Modules.- Homological Algebras.- Lie p-algebras.- Vertex Operator Algebras.ReviewsFrom the reviews: The book under review collects many classical results on representations of the Virasoro algebra and can be used both as a reference source and as a textbook. (Volodymyr Mazorchuk, Mathematical Reviews, Issue 2011 m) Author InformationTab Content 6Author Website:Countries AvailableAll regions |