Hamiltonian reduction and the construction ofq-deformed extensions of the Virasoro algebra

DOI10.1088/0305-4470/31/29/001zbMATH Open0906.17013arXivmath/9801032OpenAlexW3099601639MaRDI QIDQ4212372

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Publication date: 18 February 1999

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/9801032

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