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.

Keywords:

• renormalized powers of white noise
• w _∞-algebra
• Witt algebra
• Virasoro algebra
• Zamolodchikov algebra
• central extension of a Lie algebra

1991 Mathematics Subject Classification:

• 17B56
• 17B68
• 17B65
• 60H40

Notes

^1. URL: http://volterra.mat.uniroma2.it

^2. [email protected]

Additional information

Notes on contributors

Luigi Accardi

1. 1. URL: http://volterra.mat.uniroma2.it

Andreas Boukas

2. 2. [email protected]