Related papers: Higher order differential operators on projective …
We propose a definition of differential operators of an associative algebra $A$ in the spirit of Hochschild cohomology. Specifically we define $D(A)$ as the zero cohomology of a certain bicomplex formed by Hom-spaces…
For a smooth scheme $X$ over a perfect field $k$ of positive characteristic, we define (for each $m\in\mathbb{Z}$) a sheaf of rings $\mathcal{\widehat{D}}_{W(X)}^{(m)}$ of differential operators (of level $m$) over the Witt vectors of $X$.…
We give an explicit formula for the projectively invariant quantization map between the space of symbols of degree three and the space of third-order linear differential operators, both viewed as modules over the group of diffeomorphisms…
We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…
The $d^2$ Pauli operators attached to a composite qudit in dimension $d$ may be mapped to the vectors of the symplectic module $\mathcal{Z}_d^{2}$ ($\mathcal{Z}_d$ the modular ring). As a result, perpendicular vectors correspond to…
This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…
We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In…
We consider differential operators acting on densities of arbitrary weights on manifold $M$ identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special…
We introduce graded $\mathbb{E}_{\infty}$-rings and graded modules over them, and study their properties. We construct projective schemes associated to connective $\mathbb{N}$-graded $\mathbb{E}_{\infty}$-rings in spectral algebraic…
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…
For $\mathcal{O}$ a reduced operad, a generalized divergence from the derivations of a free $\mathcal{O}$-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the…
We investigate the holomorphic differential operators on a Riemann surface $M$. This is done by endowing $M$ with a projective structure. Let $\mathcal L$ be a theta characteristic on $M$. We explicitly describe the jet bundle $J^k(E\otimes…
Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
The algebraic notion of a differential operator on a module over a commutative ring is not extended to a module over a noncommutative ring.
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
Let $\mathcal V$ be a discrete valuation ring of mixed characteristic with perfect residue field. Let $X$ be a geometrically connected smooth proper curve over $\mathcal V$. We introduce the notion of constructible convergent…
We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are $L^p$ stable for any real number $p\in[1,\infty]$, and commute with the differential operators $\nabla$, $\nabla{\times}$, and…
The goal of this paper is to construct a calculus whose higher indices are naturally elements in the twisted K-theory groups for Lie groupoids. Given a Lie groupoid $G$ and a $PU(H)$-valued groupoid cocycle, we construct an algebra of…