  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.
