Generalized Vertex Algebras and Relative Vertex Operators: 112 (Progress in Mathematics) - Hardcover

Dong, Chongying; Lepowsky, James

Hardcover

ISBN 10: 0817637214 ISBN 13: 9780817637217

Verlag: Birkhäuser, 1993

Inhaltsangabe

The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

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The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory.

Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate one-dimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most generalof the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras.

The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 1993
• Sprache: Englisch
• ISBN 10: 0817637214
• ISBN 13: 9780817637217
• Einband: Tapa dura
• Anzahl der Seiten: 220
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar