Analytic central extensions of infinite dimensional white noise *–Lie algebras

Abstract

The connection between the *–Lie algebra of the renormalized higher powers of white noise (RHPWN) and the centreless Virasoro (or Witt)-Zamolodchikov-w ∞ *–Lie algebra of conformal field theory, as well as the associated Fock space construction, have recently been established (L. Accardi and A. Boukas, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2006), pp. 353–360; L. Accardi and A. Boukas, Int. J. Math. Comput. Sci. 1 (2006), pp. 315–342; L. Accardi and A. Boukas, (2008) J. Phys. A Math. Theor., 41, pp. 1–12; L. Accardi and A. Boukas, Comm. Stoch. Anal. 1 (2007), pp. 57–69; L. Accardi and A. Boukas, Rep. Math. Phys. 61 (2008), pp. 1–11. Available at http://arxiv.org/hep-th/0610302). In this paper, we describe a method for looking for a special class of central extensions of the RHPWN and w ∞ *–Lie algebras called ‘analytic’, i.e. central extensions where the defining cocycles can be written as formal power series of the indices of the RHPWN and w ∞ generators. Our method is also applied to the well-known Virasoro central extension of the Witt algebra.