Generalized twisted modules associated to general automorphisms of a vertex operator algebra
Twisted modules play an important crucial role in the orbifold theory of vertex operator algebras. In the paper under review, the author introduces a notion of generalized \(g\)-twisted modules, where \(g\) is not necessarily finite. When \({V=\coprod_{n\in \mathbb{Z}}V_{(n)}}\) is a vertex operator algebra such that \({V_{(0)}=\mathbb{C}\mathbf{1}}\) and \(V _{(n)} = 0\) for \(n < 0\) and \(g =\exp{({2\pi \sqrt{-1}\; {\text{Res}}_{x} Y(u, x)})}\), where \(u\) is an element of \(V\) of weight 1 such that \(L(1)u = 0\), a construction of such twisted modules is given using some \(\Delta\)-operator. In particular, examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet \(W\)-algebras are given.
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