相关论文: Gerbes of chiral differential operators. II
This note is a sequel to "Gerbes of chiral differential operators. II", math.AG/0003170. We study gerbes of chiral differential operators acting on the exterior algebra $\Lambda E$ of a vector bundle over a smooth algebraic variety $X$.…
The paper consists of two parts. In the first, we describe a way of getting from an algebra of chiral differential operators (cdo) on an abelian variety a cdo on the dual variety. The second is an introduction to the sigma-model on a torus…
In this note we study algebras of chiral differential operators over an algebraic group and over homogeneous spaces $G/G'$ where $G$ is simple and $G'$ is unipotent or parabolic.
In this note we compute the cohomological obstruction to the existence of certain sheaves of vertex algebras on smooth varieties. These sheaves have been introduced and studied in the previous work by A.Vaintrob and two of the authors.…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
We relate the gerbe of sheaves of chiral differential operators (CDO) on a algebraic variety X, studied by Gorbounov, Malikov and Schechtman, to the determinantal gerbe of the formal loop space LX introduced in our earlier paper. The liens…
There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free…
Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With…
This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.
The note complements topological aspects of the theory of chiral algebras.
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
These notes explain recent developments concerning chiral anomalies and hamiltonian quantization, their relation to the theory of gerbes, and extensions of generalized loop algebras using the residue calculus of pseudodifferential…
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the material on the derived 2-functors and the proof of the…
In this paper we will outline elements of the global calculus of seudo-differential operators on the group SU(2). This is a part of a more general approach to pseudo-differential operators on compact Lie groups that will appear in the…
We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give…
In this paper we consider successive iterations of the first-order differential operations in space ${\bf R}^3.$
Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies…