Abstract
In this article, conjugate-linear anti-involutions and θ-unitary Harish-Chandra modules over the W-algebra W(2,2) are studied. It is proved that there are only two classes that conjugate-linear anti-involutions over W(2,2). The main result of this article is that a θ-unitary Harish-Chandra module over the W-algebra W(2,2) is simply a -unitary Harish-Chandra module over the Virasoro algebra and hence is either a simple highest or lowest weight module or a simple module from the intermediate series of the form A
a,b
for some
Acknowledgements
This was supported by the National Natural Science Foundation of China (No. 10931006).