Related papers: Differential and holomorphic differential operator…
In this paper, we will look at the algebra of global differential operators $D_X$ on wonderful compactifications $X$ of symmetric spaces $G/H$ of type $A_1$ and $A_2$. We will first construct a global differential operator on these…
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
If $Q$ is a non degenerate quadratic form on ${\bb C}^n$, it is well known that the differential operators $X=Q(x)$, $Y=Q(\partial)$, and $H=E+\frac{n}{2}$, where $E$ is the Euler operator, generate a Lie algebra isomorphic to ${\go…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
We propose a sheaf-theoretic approach to the theory of differential calculi on quantum principal bundles over non-affine bases. After recalling the affine case we define differential calculi on sheaves of comodule algebras as sheaves of…
The algebraic notion of a differential operator on a module over a commutative ring is not extended to a module over a noncommutative ring.
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…
We obtain a global resolution for the sheaf of differential operators on smooth geometric quotients of free linear actions of algebraic groups. The terms of our resolution involve symmetric and alternating powers of vector bundles easily…
In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight link between invariant operators connecting modules of differential operators on…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
Denote by $SL_3(\mathbb R)$ the special linear group of degree 3 over the real numbers, $A$ the subgroup consisting of the diagonal matrices with positive entries. In this paper, we study the algebraic and analytic properties of the…
Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…
Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…
Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…
We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent…