Related papers: Operators coming from ring schemes

Let $k$ be an arbitrary field. We construct examples of regular local $k$-algebras $R$ (of positive dimension) for which the ring of differential operators $D_k(R)$ is trivial in the sense that it contains {\it no} operators of positive…

In this paper, we define and study the arithmetic of the ring of $\mathbb{U}$-operators for reductive $p$-adic groups. These operators generalise the notion of "successor" operators for trees with a marked end. We show that they are…

Let $k$ be a commutative ring and $A$ a commutative $k$-algebra. In this paper we introduce the notion of enveloping algebra of Hasse--Schmidt derivations of $A$ over $k$ and we prove that, under suitable smoothness hypotheses, the…

A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…

Following the definition of quantum differential operators given by Lunts and Rosenberg in (Sel. math., New ser. 3 (1997) 335--359), we show that the ring of quantum differential operators on the affine line is the ring generated by x and…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…

In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from Hilbert $C^{\ast}$-modules $\mathcal{H}$ to it self noted $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some propertis…

Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…

We consider generalized $\Lambda$-structures on algebras and schemes over the ring of integers $\mathit{O}_K$ of a number field $K$. When $K=\mathbb{Q}$, these agree with the $\lambda$-ring structures of algebraic K-theory. We then study…

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

We develop a theory of perfect algebraic spaces that extend the so-called perfect schemes to the setting of algebraic spaces. We prove several desired properties of perfect algebraic spaces. This extends some previous results of perfect…

Let $\mathcal{V}$ be a complete discrete valued ring of mixed characteristic $(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed to be perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be an open…

In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…

In this paper, we use trace methods to study the algebraic $K$-theory of rings of the form $R[x_1,\ldots, x_d]/(x_1,\ldots, x_d)^2$. We compute the relative $p$-adic $K$ groups for $R$ a perfectoid ring. In particular, we get the integral…

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized…

We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given…

We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…

Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin,…

An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…

By reading a standard formula for the ring of Grothendieck differential operators in a derived way, we construct a derived (sheaf of) ring of Grothendieck differential operators for Noetherian schemes $X$ separated and finite-type over a…