Contractions and central extensions of Quantum White Noise Lie algebras

  1. Luigi Accardi
  2. Andreas Boukas

Abstract

We show that the Renormalized Powers of Quantum White Noise Lie algebra RPQWN, with the convolution type renormalization δn(t − s) = δ(s)δ(t − s) of the n≥­ 2 powers of the Dirac delta function, can be obtained through a contraction of the Renormalized Powers of Quantum White Noise Lie algebra RPQWNc with the scalar renormalizationn(t) = cn−1δ(t), c > 0. Using this renormalization, we also obtain a Lie algebra W(c) which contains the w Lie algebra of Bakas and the Witt algebra as contractions. Motivated by the W algebra of Pope, Romans and Shen, we show that W(c) can also be centrally extended in a non-trivial fashion. In the case of the Witt subalgebra of W, the central extension coincides with that of the Virasoro algebra.

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Probability and Mathematical Statistics

35, z. 1, 2015

Pages from 41 to 72

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