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Twisted modules for vertex operator algebras and Bernoulli polynomials

Benjamin Doyon·James Lepowsky·Antun Milas
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Abstract

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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Benjamin Doyon, James Lepowsky, Antun Milas. 2003-06-20. Twisted modules for vertex operator algebras and Bernoulli polynomials. https://arxiv.org/abs/math/0303193

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