The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Vira...

Motivated by construction of isospin generators in particle physics (built form the SU(2) algebra), we find an equivalence between the algebra of these generators and those of the Virasoro algebra. The form of the starting generators is fixed and in order to obtain a full equivalence we introduce a new matrix product. The Cartan structure of the starting algebra is reproduced for the Virasoro-l...

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...

We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.

A bstract By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that rescaled mode defined by an integral of stress tensor T ++ on 2 plane satisfies Virasoro-like algebra when dimension scalar is large. The structure enhanced to include Kac-Moody-type if ...

It is shown that the elliptic algebra Aq,p(sl(2)c) at the critical level c = −2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p m = q c+2 for m ∈ Z, they commute when in add...

In this paper, we construct the super Witt algebra and Virasoro in framework of [Formula: see text]-deformed quantum algebras. Moreover, perform text]-algebra, text]-algebra discuss text]-Virasoro ([Formula: text] even). Besides, define another study a toy model for constraints. Relevant particular cases induced from algebras known literature are deduced formalism developed.