On the extended W-algebra of type sl2 at positive rational level

The extended W-algebra of type sl2 at positive rational level, denoted byMp+,p−, is a vertex operator algebra (VOA) that was originally proposed in [16]. This VOA is an extension of the minimal model VOA and plays the role of symmetry algebra for certain logarithmic conformal field theories. We give a construction of Mp+,p− in terms of screening operators and use this construction to prove that Mp+,p− satisfies Zhu’s c2-cofiniteness condition, calculate the structure of the zero mode algebra (also known as Zhu’s algebra), and classify all simpleMp+,p−-modules