We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra ...

In this paper, we construct the Heisenberg–Virasoro algebra in framework of R(p,q)-deformed quantum algebras. Moreover, R(p,q)-Heisenberg–Witt n-algebras is also investigated. Furthermore, generalize notion elliptic Hermitian matrix models. We use constraints to evaluate R(p,q)-differential operators Virasoro and it higher order differential operators. Particular cases corresponding algebras ex...

Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field ...

The Virasoro master equation (VME) describes the general affine-Virasoro construction T = LJaJb + iD ∂Ja in the operator algebra of the WZW model, where L ab is the inverse inertia tensor and D is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general nonlinear sigma model. The result is ...

We study the dynamics of the generalized Euler equations on Virasoro groups D̂(S1) with different Sobolev H metric (k ≥ 2) on the Virasoro algebra. We first prove that the solutions to generalized Euler equations will not blow up in finite time and then study the stability of the trivial solutions.

In this note we demonstrate that the algebra associated with coordinate transformations might contain the origins of a scalar field that can behave as an inflaton and/or a source for dark energy. We will call this particular scalar field the diffeomorphism scalar field. In one dimension, the algebra of coordinate transformations is the Virasoro algebra while the algebra of gauge transformations...

Abstract. The Virasoro–Zamolodchikov Lie algebra w∞ has been widely studied in string theory and in conformal field theory. The renormalized higher (≥ 3) powers of quantum white noise (RHPWN) algebra has been recently investigated in quantum probability. We prove that, after introducing a new renormalization technique, the RHPWN Lie algebra can be identified with a second quantization of the w∞...