A Pseudo-Conformal Representation of the Virasoro Algebra

A pseudo–conformal representation of the Virasoro algebra

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo–conformal representation. In special cases, this representation reduces to ordinary– or logarithmic–conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary– or logarithmic–conformal field theories. This representat...

Conformal Mechanics and the Virasoro Algebra

We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.

R – Conformal Symmetries in 2 D Nonlocal Quantum Field Theory , Categorical Representation Theory , and Virasoro Algebra

Lie triple derivation algebra of Virasoro-like algebra

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

The Virasoro algebra

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...