Hamiltonian Reduction and the Construction of q-Deformed Extensions of the Virasoro Algebra

Details Hamiltonian Reduction and the Construction of q-Deformed Extensions of the Virasoro Algebra Hamiltonian Reduction and the Construction of q-Deformed Extensions of the Virasoro Algebra

1998-01-07

arxiv.org/abs/math/9801032v1

Mathematics

Quantum Algebra

6 pages, latex

Scientific paper

10.1088/0305-4470/31/29/001

In this paper we employ the construction of Dirac bracket for the remaining current of $sl(2)_q$ deformed Kac-Moody algebra when constraints similar to those connecting the $sl(2)$-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced, in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

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