Representation Theory of the Virasoro Algebra [recurso electrónico] / by Kenji Iohara, Yoshiyuki Koga.

Por: Iohara, Kenji [author.]Colaborador(es): Koga, Yoshiyuki [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Springer Monographs in MathematicsEditor: London : Springer London, 2011Descripción: XVIII, 474 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9780857291608Tema(s): Mathematics | Algebra | Topological Groups | Functions, special | Combinatorics | Mathematics | Algebra | Non-associative Rings and Algebras | Theoretical, Mathematical and Computational Physics | Topological Groups, Lie Groups | Special Functions | CombinatoricsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512 Clasificación LoC:QA150-272Recursos en línea: Libro electrónicoTexto
Contenidos:
Preliminary -- 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.
En: Springer eBooksResumen: The 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. Fundamental results are organized in a unified way and existing proofs refined. 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.
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Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA150 -272 (Browse shelf(Abre debajo)) 1 No para préstamo 370502-2001

Preliminary -- 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.

The 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. Fundamental results are organized in a unified way and existing proofs refined. 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.

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