The level one zhu algebra for the virasoro vertex operator algebra

The level one Zhu algebra for the Virasoro vertex operator algebra is constructed, and implications for the use of Zhu algebras of higher level for vertex operator algebras are discussed. In particular, we show that the level one Zhu algebra gives rise to new indecomposable non simple modules for the Virasoro vertex operator algebra not detected by or induced from the level zero Zhu algebra.