The method of constrained Hamiltonian systems can be used to reduce Fock modules. It is applied to the Virasoro algebra, where a possibly new realization is found.

In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.

In a previous paper by the authors, we obtain first example of finitely freely generated simple Z-graded Lie conformal algebra linear growth that cannot be embedded into any general algebra. this paper, obtain, as byproduct, another class such algebras classifying G=⊕i=−1∞Gi satisfying following, G0≅Vir, Virasoro algebra; Each Gi for i≥−1 is Vir-module rank one.

We show that the (semi-infinite) Ablowitz–Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508–1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Velázquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29–56] and their action on ...

Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g ⊕ g+, and let s and t be commuting formal variables commuting with g. We prove that the map C : sg[[s, t]] × tg+[[s, t]] −→ sg[[s, t]] ⊕ tg+[[s, t]] defined by the Campbell-Baker-Hausdorff formula and given by e − e + = eC(sg ,tg) for g ∈ g[[s, t]] is a bijection, as is well known when g ...

The superselection structure of so(N) WZW models is investigated from the point of view of algebraic quantum field theory. At level 1 it turns out that the observable algebras of the WZW theory can be constructed in terms of even CAR algebras. This fact allows to give a formulation of these models close to the DHR framework. Localized endomorphisms are constructed explicitly in terms of Bogoliu...

Vertex operator algebras (VOA) were introduced by Borcherds ( [B] ) as an axiomatic description of the ‘holomorphic part’ of a conformal field theory ( [BPZ] ). An account of the theory of vertex operator algebras may be found in [FLM]. One of the most important examples of VOAs ( [FZ] ) is the Virasoro VOAs, i.e.VOAs corresponding to the representations of the Virasoro algebra L, denoted by Vc...

We review the deformed W -algebra Wq,t(ŝlN ) and its screening currents. We explicitly construct the Local Integrals of Motion In (n = 1, 2, · · ·) for this deformed W -algebra. We explicitly construct the Nonlocal Integrals of Motion Gn (n = 1, 2, · · ·) by means of the screening currents. Our Integrals of Motion commute with each other, and give the elliptic version of those for the Virasoro ...

The fractional supersymmetry chiral algebras, A(K), in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K). We show that associativity and closure of A(K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of the A(K) algebras explicitly and we sho...

We comment on the conformal boundary states of the c=1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on the fundamental boundary states at the self-dual radius. We further calculate the boundary entropy and find that the Virasoro boundary states at irrational rad...