Related papers: A direct formulation of Dieudonn\'e module theory
In this note we describe a seemingly new approach to the complex representation theory of the wreath product $G\wr S_d$ where $G$ is a finite abelian group. The approach is motivated by an appropriate version of Schur-Weyl duality. We…
Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.
The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other…
Liouvillian systems were initially introduced within the framework of differential algebra. They can be seen as a natural extension of differential flat systems. Many physical non flat systems seem to be Liouvillian. We present in this…
We define a convenient $\infty$-operad parametrizing modules over commutative algebras in $\infty$-categories.
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…
Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the…
The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$-modules. To do this, we calculate explicitly an isomorphism between canonical sheaves defined abstractly. Using this…
For a ring $A$ there is a well-known duality between definable subcategories of right $A$-modules and definable subcategories of left $A$ modules. This is a consequence of Auslander-Gruson-Jensen duality $\rm…
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…
This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible…
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
We give a definition of an amenable fusion module over a fusion algebra. A notion of relative integrability for the `coduals' of coideals of compact quantum groups was recently introduced in the joint work of de Commer and Dzokou Talla. We…