For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1 ...

Virasoro algebra possesses a representation in the tangent space to the space of normalized univalent functions defined in the unit disk and smooth on its boundary. We discuss connections between representations of the Virasoro algebra and the Löwner-Kufarev equations in partial and ordinary derivatives. Virasoro generators turn to be conservative quantites for the Löwner-Kufarev ODE, and the L...

We consider the M(2, 3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We construct an algebra of operators acting on the BRST cohom...

The present paper is another step toward the classification of ZZ×ZZ-graded Lie algebras: we classify ZZ×ZZ-graded Lie algebras A = ⊕i,j∈ZZAi,j over a field IF of characteristic 0 with dimAi,j ≤ 1 for i, j ∈ ZZ, satisfying: (1) A0 = ⊕i∈ZZAi,0 ≃ Vir, the centerless Virasoro algebra, (2) A0,−1,A0,0,A0,1 span the 3-dimensional simple Lie algebra sl2, (3) A is generated by the centerless Virasoro a...

It was shown by Brown and Henneaux that the classical theory of gravity on AdS3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory onAdS3. In this paper, we explore various aspects of string theory on AdS3 and study the relation between thes...

It was shown by Brown and Henneaux that the classical theory of gravity on AdS3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory on AdS3. In this paper, we explore various aspects of string theory on AdS3 and study the relation between the...

For every p ≥ 2, we obtained an explicit construction of a family of W(2, 2p − 1)-modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual W(2, 2p − 1)-modules, we described their internal structure, and computed their graded dimensions. In addition, we constructed certain hidden logarithmic intertwining operators among two ...

An eighth-order equation in $$(3+1)$$ dimension is studied for its integrability. Its symmetry group shown to be infinite-dimensional and checked Virasoro-like structure. The have no Painlev $$\acute{\mathrm{e}}$$ property. One- two-dimensional classifications of algebra are also given.

We present a fractional superspace formulation of the centerless parasuper-Virasoro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by t and θ, with t a real coordinate and θ a paragrassmann variable of order M a...

We investigate in details how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic rela...