Twisted modules for vertex operator algebras and Bernoulli polynomials

Doyon, Benjamin; Lepowsky, James; Milas, Antun

Twisted modules for vertex operator algebras and Bernoulli polynomials

Authors

Doyon, Benjamin

Lepowsky, James

Milas, Antun

Description

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. This is explained through results in the general theory of vertex operator algebras, including a new identity, which we call ``modified weak associativity.'' This paper is an announcement. The detailed proofs will appear elsewhere.
15 pages, LaTeX, Revised version (to appear in I.M.R.N.)