Related papers: On a Commutative Ring of Two Variable Differential…

We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…

Let $R$ be a commutative ring with identity. The paper studies the problem of self-orthogonality and self-duality matrix-product codes (MPCs) over $R$. Some methods as well as special matrices are introduced for the construction of such…

We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix…

In this paper, we study the unit dot graph of product of commutative rings

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notion of morphic modules over a commutative ring.

We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function…

There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…

We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism,…

Regarding polynomial functions on a subset $S$ of a non-commutative ring $R$, that is, functions induced by polynomials in $R[x]$ (whose variable commutes with the coefficients), we show connections between, on one hand, sets $S$ such that…

We characterize the idempotent stable range one $2\times 2$ matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and examples complete the subject.

We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.

The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most…

We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhibit such a moduli space admitting two small…

If $k$ is a field and $R$ is a commutative $k$-algebra, we explore the question of when the ring $D_{R|k}$ of $k$-linear differential operators on $R$ is isomorphic to its opposite ring. Under mild hypotheses, we prove this is the case…

We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.

We compute a presentation for the integral Chow rings of the moduli stacks of degree $2$ maps from smooth rational curves to projective space $\mathbb{P}^r$, as a quotient of a three-variable polynomial ring. The relations as $r$ varies…

We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra ($q$-analogue…

In this paper we propose a very effective method for constructing matrix commuting differential operators of rank 2 and vector rank (2,2). We find new matrix commuting differential operators L, M of orders 2 and 2g respectively.

We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat…

A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…