Twisted modules for vertex operator algebras and Bernoulli polynomials

Details Twisted modules for vertex operator algebras and Bernoulli polynomials Twisted modules for vertex operator algebras and Bernoulli polynomials

2003-03-16

arxiv.org/abs/math/0303193v2

Mathematics

Quantum Algebra

15 pages, LaTeX, Revised version (to appear in I.M.R.N.)

Scientific paper

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.

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