The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal transformations of two-dimensional space (r − t s...

Itô calculus has been generalized in white noise analysis and in quantum stochastic calculus. Quantum white noise calculus is a third generalization, unifying the two above mentioned ones and bringing some unexpected insight into some old problems studied in different fields, such as the renormalization problem in physics and the representation theory of Lie algebras. The present paper is an at...

The Mickelsson-Faddeev (MF) algebra can naturally be embedded in a non-Lie algebra, which suggests that it has no Fock representations. The difficulties are due to the inhomogeneous term in the connection’s transformation law. Omitting this term yields a “classical MF algebra”, which has other abelian extensions that do possess Fock modules. I explicitly construct such modules and the intertwin...

We consider representations of the Virasoro algebra, a one-dimensional central extension of the Lie algebra of vectorfields on the unit circle. Positive-energy, highest weight and Verma representations are defined and investigated. The Shapovalov form is introduced, and we study Kac formula for its determinant and some consequences for unitarity and degeneracy of irreducible highest weight repr...

<p style='text-indent:20px;'>In this paper, we characterize the graded post-Lie algebra structures on Schrödinger-Virasoro Lie algebra. Furthermore, as an application, obtain all homogeneous Rota-Baxter operator of weight <inline-formula><tex-math id="M1">$ 1 $</tex-math></inline-formula> algebra.</p>

We show that the continuous limit of a wide natural class of the right-invariant discrete Lagrangian systems on the Virasoro group gives the family of integrable PDE’s containing Camassa-Holm, Hunter-Saxton and Korteweg-de Vries equations. This family has been recently derived by Khesin and Misio-lek as Euler equations on the Virasoro algebra for H1 α,βmetrics. Our result demonstrates a univers...

The (p+, p−) singlet algebra is a vertex operator algebra that is strongly generated by a Virasoro field of central charge 1− 6(p+− p−) /p+p− and a single Virasoro primary field of conformal weight (2p+−1)(2p−−1). Here, the modular properties of the characters of the uncountably many simple modules of each singlet algebra are investigated and the results used as the input to a continuous analog...