AuthorLepowsky, James. author
TitleIntroduction to Vertex Operator Algebras and Their Representations [electronic resource] / by James Lepowsky, Haisheng Li
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004
Connect tohttp://dx.doi.org/10.1007/978-0-8176-8186-9
Descript XIII, 318 p. online resource

CONTENT

1 Introduction -- 1.1 Motivation -- 1.2 Example of a vertex operator -- 1.3 The notion of vertex operator algebra -- 1.4 Simplification of the definition -- 1.5 Representations and modules -- 1.6 Construction of families of examples -- 1.7 Some further developments -- 2 Formal Calculus -- 2.1 Formal series and the formal delta function -- 2.2 Derivations and the formal Taylor Theorem -- 2.3 Expansions of zero and applications -- 3 Vertex Operator Algebras: The Axiomatic Basics -- 3.1 Definitions and some fundamental properties -- 3.2 Commutativity properties -- 3.3 Associativity properties -- 3.4 The Jacobi identity from commutativity and associativity -- 3.5 The Jacobi identity from commutativity -- 3.6 The Jacobi identity from skew symmetry and associativity -- 3.7 S3-symmetry of the Jacobi identity -- 3.8 The iterate formula and normal-ordered products -- 3.9 Further elementary notions -- 3.10 Weak nilpotence and nilpotence -- 3.11 Centralizers and the center -- 3.12 Direct product and tensor product vertex algebras -- 4 Modules -- 4.1 Definition and some consequences -- 4.2 Commutativity properties -- 4.3 Associativity properties -- 4.4 The Jacobi identity as a consequence of associativity and commutativity properties -- 4.5 Further elementary notions -- 4.6 Tensor product modules for tensor product vertex algebras -- 4.7 Vacuum-like vectors -- 4.8 Adjoining a module to a vertex algebra -- 5 Representations of Vertex Algebras and the Construction of Vertex Algebras and Modules -- 5.1 Weak vertex operators -- 5.2 The action of weak vertex operators on the space of weak vertex operators -- 5.3 The canonical weak vertex algebra ?(W) and the equivalence between modules and representations -- 5.4 Subalgebras of ?(W) -- 5.5 Local subalgebras and vertex subalgebras of ?(W) -- 5.6 Vertex subalgebras of ?(W) associated with the Virasoro algebra -- 5.7 General construction theorems for vertex algebras and modules -- 6 Construction of Families of Vertex Operator Algebras and Modules -- 6.1 Vertex operator algebras and modules associated to the Virasoro algebra -- 6.2 Vertex operator algebras and modules associated to affine Lie algebras -- 6.3 Vertex operator algebras and modules associated to Heisenberg algebras -- 6.4 Vertex operator algebras and modules associated to even latticesโthe setting -- 6.5 Vertex operator algebras and modules associated to even latticesโthe main results -- 6.6 Classification of the irreducible L?(?, O)-modules for g finite-dimensional simple and ? a positive integer -- References


SUBJECT

  1. Mathematics
  2. Algebra
  3. Associative rings
  4. Rings (Algebra)
  5. Topological groups
  6. Lie groups
  7. Operator theory
  8. Physics
  9. Mathematics
  10. Algebra
  11. Associative Rings and Algebras
  12. Operator Theory
  13. Topological Groups
  14. Lie Groups
  15. Theoretical
  16. Mathematical and Computational Physics