Related papers: Differential Operators on the free algebras
In the present paper, we propose the concepts of weighted differential ($q$-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are constructed, in both the commutative and noncommutative contexts.
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…
We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
A duality transform for the coalgebra of the free difference quotient derivation-multiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic…
A model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T.…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
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…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
We are interested in the evolution operators defined on commutative and nonassociative algebras when the scalar field is of characteristic 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic and plenary train…
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…
A Rota-Baxter operator defined on the polynomial algebra is called monomial if it maps each monomial to a monomial with some coefficient. We classify monomial Rota-Baxter operators defined on the algebra of polynomials in one variable…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.