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We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.

In this paper, we study the generalized derivation of a Lie sub-algebra of the Lie algebra of polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant vector fields and the Euler vector field, under some conditions…

Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the non-trivial correlations…

A complete classification of two-dimensional algebras over algebraically closed fields is provided

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…

This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.

Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a…

Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…

We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular orbifold of generalized elliptic curves whose sections are…

We classify all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero. As a corollary, we deduce the classification of all linearly compact unital simple generalized Poisson superalgebras.

We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory we give a proof of a result of Helmke, Jordan and Lieb on the number of linear unimodular matrix polynomials over a finite…

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…

We study ordinary differential equations in the complex domain given by meromorphic vector fields on K\"ahler compact complex surfaces. We prove that if such an equation has a maximal single valued solution with Zariski-dense image (in…

The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…