# Introduction to Vertex Operator Algebras and Their Representations

Springer Science & Business Media, 2004 - 318 páginas
Vertex 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.

### O que estão dizendo -Escrever uma resenha

Não encontramos nenhuma resenha nos lugares comuns.

### 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 L 289 LI 315 Direitos autorais

### Sobre o autor (2004)

James Lepowsky is Professor in the Department of Mathematics at Rutgers University, New Jersey.