0 −→ c −→ g1 φ1 −→g −→ 0 such that c ⊆ Z(g1), the center of g̃. A morphism of central extensions is a Lie algebra homomorphism ψ : g1 → g2 such that φ2ψ = φ1. A universal central extension is a central extension g̃ such that there is a unique morphism from g̃ to every other central extension of g. The Schur multiplier is the kernel of the universal central extension of g. It classifies the project...

A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations. [email protected], [email protected], [email protected]

We use recently derived explicit formulae for the Virasoro algebra’s singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the action of the singular vectors on conformal fields.

Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing N v fermion species of equal masses, we next use the Virasoro constraints to compute two (low-mass and large-mass) expansions of the partially quenched chiral condensate through the replica method of lett...

In low dimensional gravity on anti-de sitter space there exists a possibility that the asymptotic isometry is raised to a Virasoro symmetry living at spatial infinity. We discuss in detail asymptotic isometry of the most general anti-de sitter dilaton gravity in two dimensions. From analysis of the boundary dynamics it turns out that the Virasoro symmetry is not preserved in all the models. Mor...

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...