  In his landmark paper, Zhu associated two associative algebras to a vertex
operator algebra: what are now called Zhu's algebra and the C_2-algebra. The
former has a nice interpretation in terms of the representation theory of the
VOA, while the latter only serves as a finiteness condition. In this paper we
undertake first steps to unravel the interpretation of the C_2 vector space. In
particular we suggest that it seems and controls the twisted representations of
the VOA.
