Related papers: External zonotopal algebra
We show that the class of Metropolis-Rota implication algebras can be given a universal axiomatization using an operation closely related to composition in oriented matroids. Lastly we describe the role of our new operation in the collapse…
The basic concepts underlying our analysis of {\it W-algebras} as extended symmetries of integrable systems are summarized. The construction starts from the second hamiltonian structure of ``Generalized Drinfel'd-Sokolov'' hierarchies, and…
In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…
We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a…
We study generalized inverses for matrices associated with double star digraphs. Explicit block formulas and existence criteria are obtained for core, dual core, core EP, and dual core EP inverses, expressed in terms of explicit algebraic…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
We establish results about algebraic shifting of simplicial complexes and use them to compare different shifting operations. In particular, we show that each shifting operation does not decrease the number of facets, and that the exterior…
We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of…
For every system $\{ p_n(z) \}_{n=0}^\infty$ of OPRL or OPUC, we construct Sobolev orthogonal polynomials $y_n(z)$, with explicit integral representations involving $p_n$. Two concrete families of Sobolev orthogonal polynomials (depending…
Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie…
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
We study some Lie algebras defined by solutions to the double shuffle equations with poles and construct families of explicit solutions to these equations in all weights and depths. These provide universal coordinates in which to write down…
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of regularity for such algebras.
Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as…
We discuss globalization for geometric partial comodules in a monoidal category with pushouts and we provide a concrete procedure to construct it, whenever it exists. The mild assumptions required by our approach make it possible to apply…