相关论文: Residues and Differential Operators on Schemes
A notion of rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in C^n is introduced. It is proved that BA function exists only for very special configurations (locus configurations), which satisfy certain…
Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such…
Let $R$ be a commutative ring: we explain the Beilinson-Bernstein localisation mechanism for sheaves of homogeneous twisted differential operators defined over a smooth, separated, locally of finite type $R$-scheme. As an application, we…
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
There is a commutative algebra of differential-difference operators, acting on polynomials on R_2, associated with the reflection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free…
Let \pi : X -> S be a finite type morphism of noetherian schemes. A smooth formal embedding of X (over S) is a bijective closed immersion X -> \frak{X}, where \frak{X} is a noetherian formal scheme, formally smooth over S. An example of…
A sequence is difference algebraic (or D-algebraic) if finitely many shifts of its general term satisfy a polynomial relationship; that is, they are the coordinates of a generic point on an affine hypersurface. The corresponding equations…
This paper investigates residue maps and their spanning properties for singular algebraic curves, with particular emphasis on three interconnected themes: the \emph{scheme--theoretic residue span}, the \emph{residue--balancing principle},…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form…
On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…
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…
Let $V$ be a smooth scheme over a field $k$, and let $\{I_n, n\geq 0\}$ be a filtration of sheaves of ideals in $\calo_V$, such that $I_0=\calo_V$, and $I_s\cdot I_t\subset I_{s+t}$. In such case $\bigoplus I_n$ is called a Rees algebra. A…
We start studying chiral algebras (as defined by A. Beilinson and V. Drinfeld) from the point of view of deformation theory. First, we define the notion of deformation of a chiral algebra on a smooth curve $X$ over a bundle of local…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…