We define an elliptic deformation of the Virasoro algebra. We conjecture that the [Formula: see text] Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special points in the moduli space the 6d Nekrasov partition function reduces to the partition function of a 4d vortex theory supported on [Formula: see text], which is in turn ...

A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and its suitable representation. The embedding into algebras of in analogue to the classical Jordan—Schwinger map. number examples such computed. In particular, we obtain twisted Heisenberg-Virasoro Schrödinger-Virasoro among others. More generally, construct an arbitrary locally convex t...

Abstract. In this paper we investigate Lie bialgebra structures on a twisted Schrödinger-Virasoro type algebra L. All Lie bialgebra structures on L are triangular coboundary, which is different from the relative result on the original Schrödinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to L⊗L and we develop ...

Representations of the twisted Heisenberg-Virasoro algebra at level zero. Abstract. We describe the structure of the irreducible highest weight modules for the twisted Heisenberg-Virasoro Lie algebra at level zero. We prove that such a module is either isomorphic to a Verma module or to a quotient of two Verma modules.

Based on the quantum superspace construction of q-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the q-W∞ algebra recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super-Virasoro algebra as well as their osp(1, 2) subalgebras. Applying our quantum superspace structure to conformal f...

We study conformal biderivations of a Lie algebra. First, we give the definition biderivation. Next, determine loop W(a, b) algebra, Virasoro and Especially, all on algebra are inner biderivations.