I. J. Lautenschleguer

arXiv1998

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

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.

math.QA↗

arXiv1996

Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra

The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of ${\cal{U}}_{q} ({\widehat{su}}(2))$ quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to ${\cal{U}}_{q} ({\widehat{su}}(N+1))$ is also proposed.

q-alg↗