It is shown that the ternary Virasoro-Witt algebra of Curtright, Fairlie and Zachos can be constructed by applying the Nambu commutator to the vect(1) realization on scalar densities. This construction is generalized to vect(d), but the corresponding 3-algebra fails to close. There has recently been a surge of interest in 3-algebras in M-theory [1, 2, 3, 4], which is closely related to the tern...

Virasoro-type symmetries and their roles in solvable models are reviewed. These symmetries are described by the two-parameter Virasoro-type algebra Virp,q by choosing the parameters p and q suitably. Based on talks presented by H.A. and J.S. at the Nankai-CRM joint meeting on the quantum deformed Virasoro algebra, Tianjin, China, August 19-24, 1996. To appear in the CRM series in mathematical p...

In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are obtained.

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]

In this lecture we discuss ‘beyond CFT’ from symmetry point of view. After reviewing the Virasoro algebra, we introduce deformed Virasoro algebras and elliptic algebras. These algebras appear in solvable lattice models and we study them by free field approach.

The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional bl...

Within the framework of a local expansion of the logarithm of the O(N) σmodel vacuum functional, valid for slowly varying fields, the modified Virasoro algebra is studied. The operator-like central charge term is given, up to second order, for a general functional. Typeset using REVTEX ∗Email address: [email protected]

The manifest expression for a (Virasoro-like) infinite-dimensional generalization of the 3 + 1-dimensional conformal algebra so(4, 2) is presented in this letter. It provides the arena for integrable models of Anti-de Sitter and conformal gauge theories of higher-generalized-spin fields in realistic dimensions.

Within the framework of a local expansion of the logarithm of the O(N) σmodel vacuum functional, valid for slowly varying fields, the modified Virasoro algebra is studied. The operator-like central charge term is given, up to second order, for a general functional. Typeset using REVTEX ∗Email address: [email protected]