Related papers: Virasoro extensions for diffeomorphisms with break…
In this paper we investigate Lie bialgebra structures on the deformative Schr\"{o}dinger-Virasoro algebras mainly using the techniques introduced recently by Liu, Pei and Zhu, which indicate that all cases considered in this paper except…
Let $A_n=\mathbb{C}[t_i^{\pm1},~1\leq i\leq n]$ be the algebra of Laurent polynomials in $n$-variables. Let $\mu=(\mu_1,\ldots,\mu_n)$ be a generic vector in $\mathbb{C}^n$ and $\Gamma_{\mu}=\{\mu\cdot\alpha,\alpha\in \mathbb{Z}^n\}$ where…
We prove the so called Liv\v{s}ic theorem for cocycles taking values in the group of $C^{1+\beta}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global…
On a real ($\mathbb F=\mathbb R$) or complex ($\mathbb F=\mathbb C$) analytic connected 2-manifold $M$ with empty boundary consider two vector fields $X,Y$. We say that $Y$ {\it tracks} $X$ if $[Y,X]=fX$ for some continuous function…
Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra DRO(N) be the extension of $diff(N)\oplus diff(1)$ by its four inequivalent Virasoro-like cocycles. Here $diff(N)$ is the diffeomorphism algebra in $N$-dimensional spacetime…
In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…
We study rigidity and stability of infinite dimensional algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes,…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.
Horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on prolongation of a Lie algebroid are considered. Then using exact sequences, semisprays are constructed. Moreover, important geometrical objects…
This article is concerned with an extensive study of an infinite-dimensional Lie algebra $\mathfrak{sv}$, introduced in the context of non-equilibrium statistical physics, containing as subalgebras both the Lie algebra of invariance of the…
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf-theoretic Virasoro constraints in terms of…
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket such that the anchor is compatible with the Lie bracket of vector fields. We firstly show how most geometrical structures intensively studied in the framework of…
In this paper we present all the Leibniz 2-cocycles of the twisted Schr\"{o}dinger-Virasoro algebra, which determine its second Leibniz cohomology group.
We establish a new universal relation between the Lie bracket and $\circ$-multiplication of tangent fields on any Frobenius (super)manifold. We use this identity in order to introduce the notion of ``weak Frobenius manifold'' which does not…
We present a deformation theory approach to the classification of kinematical Lie algebras in 3+1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical Lie algebra and of its…
We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and…
We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over a fibred manifold to a convenient Lie algebroid over a…
We show that the deformations of Virasoro and super Virasoro algebra, constructed earlier on an abstract mathematical background, emerge after Wick rotation, within an exact treatment of discrete-time free field models on a circle. The…