相关论文: Determination of the 2- cocycles for the three poi…
In this paper, we establish an explicit classification of length two extensions of tensor modules for the Witt algebra using the cohomology of the Witt algebra with coefficients in the module of the space of homomorphisms between the two…
In this paper, we classify 1-cocycles of the Witt algebra with coefficients in the tensor product of two arbitrary tensor density modules. In a special case, we recover a theorem originally established by Ng and Taft in \cite{NT}.…
We define a 3-point Virasoro algebra, and construct a representation of it on a previously defined Fock space for the 3-point affine algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left( \Omega_{\mathcal R}/d{\mathcal R}\right)$.
We formalize in Lean certain calculational proofs about infinite-dimensional Lie algebras. Specifically, we construct the Virasoro algebra as a central extension of the Witt algebra associated with a nontrivial 2-cocycle, and we construct…
In a series of papers by Henkel, Roger and Unterberger, Schr\"{o}dinger-Virasoro algebras and their deformations were introduced and investigated. In the present paper we determine the 2-cocycles of a class of deformative…
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.
It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…
Multi-point algebras of Krichever Novikov type for higher genus Riemann surfaces are generalisations of the Virasoro algebra and its related algebras. Complete existence and uniqueness results for local 2-cocycles defining almost-graded…
In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern (and Segre) classes of all tautological bundles on it and compute the nef…
Both original and twisted Schr\"{o}dinger-Virasoro algebras also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim to determine the 2-cocycles of original…
The main aim of this article is to prove the one-dimensionality of the third algebraic cohomology of the Virasoro algebra with values in the adjoint module. We announced this result in a previous publication with only a sketch of the proof.…
We determine all $\delta$-biderivations for the Witt algebra, the Virasoro algebra, the $W$-algebras $W(a,b)$ and their universal central extensions $\widetilde W(a,b)$, and then give some applications.
In this paper, we compute the entire cyclic cohomology of noncommutative 3-spheres. First of all, we verify the Mayer-Vietoris exact sequence of entire cyclic cohomology in the framework of Fr\'echet $^*$-algebras. Applying it to their…
In this article, we revisit some aspects of the computation of the cohomology class of $H^2 ( \text{Witt}, \mathbb{C})$ using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
The derivation algebras, automorphism groups and second cohomology groups of the generalized loop Schr\"{o}dinger-Virasoro algebras are completely determined in this paper.
We define certain higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums, and show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications.…
We approach the question of complexification of the diffeomorphism group of the circle by considering real-analytic maps from the circle into the punctured complex plane with winding number +1. Such complex deformations form an…
The Virasoro operations in Witten's theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur's ring \Delta of…
We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution…