We consider the enhancement of SL(2, R) to Virasoro algebra in a system ofN particles on AdS2. We restrict our discussion to the case of non-interacting particles, and argue that they must be treated as fermions. We find operators Ln whose commutators on the ground state, |vac〉, satisfy relations that are reminisent of c = 1 Virasoro algebra, provided N ≥ n ≥ −N . Same relations hold also on th...

I discuss a realization of stress-tensor for parafermion theories following the generalized Frenkel-Kac construction for higher level Kac-Moody algebras. All the fields are obtained from d=rank free bosons compactified on torus. This gives an alternative realization of Virasoro algebra in terms of a non-local correction of a free field construction which does not fit the usual background charge...

We investigate new realisations of the W 3 algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with c = 102 and c = 100 to build non-critical and critical W 3 BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string...

In this paper we analyze one–matrix models by means of the associated discrete linear systems. We see that the consistency conditions of the discrete linear system lead to the Virasoro constraints. The linear system is endowed with gauge invariances. We show that invariance under time–independent gauge transformations entails the integrability of the model, while the double scaling limit is con...

The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted algebra. Lie bialgebras play an important role in searching for solutions quantum Yang–Baxter equations. It is interesting to study bialgebra structures on Since brackets are different from that and Virasoro-like algebras, there inner derivations (from itself its tensor space) which hidden more deeply inte...