Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorDong, Chongying. author
TitleGeneralized Vertex Algebras and Relative Vertex Operators [electronic resource] / by Chongying Dong, James Lepowsky
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1993
Connect to
Descript IX, 206 p. online resource


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 general of 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


1 Introduction -- 2 The setting -- 3 Relative untwisted vertex operators -- 4 Quotient vertex operators -- 5 A Jacobi identity for relative untwisted vertex operators -- 6 Generalized vertex operator algebras and their modules -- 7 Duality for generalized vertex operator algebras -- 8 Monodromy representations of braid groups -- 9 Generalized vertex algebras and duality -- 10 Tensor products -- 11 Intertwining operators -- 12 Abelian intertwining algebras, third cohomology and duality -- 13 Affine Lie algebras and vertex operator algebras -- 14 Z-algebras and parafermion algebras -- List of frequently-used symbols, in order of appearance

Mathematics Algebra Associative rings Rings (Algebra) Group theory Topological groups Lie groups Operator theory Physics Mathematics Algebra Associative Rings and Algebras Operator Theory Group Theory and Generalizations Topological Groups Lie Groups Theoretical Mathematical and Computational Physics


Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network


facebook   instragram