COHOMOLOGY OF THE VIRASORO–ZAMOLODCHIKOV AND RENORMALIZED HIGHER POWERS OF WHITE NOISE *-LIE ALGEBRAS

We prove the triviality of the second cohomology group of the Virasoro–Zamolodchikov and Renormalized Higher Powers of White Noise *-Lie algebras. It follows that these algebras admit only trivial central extensions. We also prove that the Heisenberg–Weyl *-Lie algebra admits nontrivial central extensions which are parametrized in a 1-to-1 way by ℂ\{0}. Explicit unitary *-representations of these extensions and their implications for our renormalization program are discussed in Ref. 8.