## Introduction to Vertex Operator Algebras and Their RepresentationsVertex operator algebra theory is a new area of mathematics. It has been an exciting and ever-growing subject from the beginning, starting even before R. Borcherds introduced the precise mathematical notion of "vertex algebra" in the 1980s [BI]. Having developed in conjunction with string theory in theoretical physics and with the theory of "monstrous moonshine" and infinite-dimensional Lie algebra theory in mathematics, vertex (operator) algebra theory is qualitatively different from traditional algebraic theories, reflecting the "nonclassical" nature of string theory and of monstrous moonshine. The theory has revealed new perspectives that were unavailable without it, and continues to do so. "Monstrous moonshine" began as an astonishing set of conjectures relating the Monster finite simple group to the theory of modular functions in number theory. As is now known, vertex operator algebra theory is a foundational pillar of monstrous moonshine. With the theory available, one can formulate and try to solve new problems that have far-reaching implications in a wide range of fields that had not previously been thought of as being related. This book systematically introduces the theory of vertex (operator) algebras from the beginning, using "formal calculus," and takes the reader through the fundamental theory to the detailed construction of examples. The axiomatic foundations of vertex operator algebras and modules are studied in detail, general construction theorems for vertex operator algebras and modules are presented, and the most basic families of vertex operator algebras are constructed and their irreducible modules are constructed and are also classified. The construction theorems for algebras and modules are based on a study of representations of a vertex operator algebra, as opposed to modules for the algebra, as developed in [Li3]. A significant feature of the theory is that in general, the construction of modules for (or representations of) a vertex operator algebra is in some sense more subtle than the construction of the algebra itself. With the body of theory presented in this book as background, the reader will be well prepared to embark on any of a vast range of directions in the theory and its applications. |

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### Conteúdo

II | 1 |

III | 5 |

IV | 8 |

V | 12 |

VI | 13 |

VII | 15 |

VIII | 17 |

IX | 21 |

XXIX | 124 |

XXX | 127 |

XXXI | 128 |

XXXII | 137 |

XXXIII | 138 |

XXXIV | 141 |

XXXV | 145 |

XXXVI | 148 |

XI | 29 |

XII | 33 |

XIII | 49 |

XV | 65 |

XVI | 72 |

XVII | 81 |

XVIII | 84 |

XIX | 86 |

XX | 92 |

XXI | 94 |

XXII | 98 |

XXIII | 101 |

XXIV | 105 |

XXV | 111 |

XXVI | 117 |

XXVII | 118 |

XXVIII | 121 |

XXXVII | 151 |

XXXVIII | 156 |

XXXIX | 163 |

XL | 165 |

XLI | 173 |

XLII | 179 |

XLIII | 191 |

XLIV | 193 |

XLV | 201 |

XLVI | 217 |

XLVII | 226 |

XLVIII | 239 |

XLIX | 264 |

289 | |

315 | |

### Outras edições - Visualizar todos

Introduction to Vertex Operator Algebras and Their Representations James Lepowsky,Haisheng Li Visualização parcial - 2004 |

Introduction to Vertex Operator Algebras and Their Representations James Lepowsky,Haisheng Li Visualização parcial - 2012 |

Introduction to Vertex Operator Algebras and Their Representations James Lepowsky,Haisheng Li Visualização de trechos - 2004 |

### Termos e frases comuns

affine Lie algebra algebra of central algebra structure algebras and modules analogue axioms central charge central extension commutative associative algebra complex number conformal field theory conformal vector construction Corollary creation property defined definition delta function endomorphism equivalent exists fact finite finite-dimensional FLM6 formal Laurent series formal series formal variables g-module of level grading restrictions h e h holds irreducible module isomorphism Jacobi identity lattice Lg(t linear map Lw(x moonshine module natural nonnegative integer nonzero notation notion of module notion of vertex operator algebra theory prove rational functions recall Remark restricted module result scalar Section skew symmetry submodule subset subspace tensor product Theorem truncation condition unique vacuum vector vector space vertex algebra structure vertex operator algebra vertex operator subalgebra Vg(t Virasoro algebra weak associativity weak vertex algebra weak vertex operator weak vertex subalgebra Yw(v Z-graded