Related papers: Dimension and decomposition in modular upper-conti…
We classify the module categories over the double (possibly twisted) of a finite group.
We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
It is shown that the coincidence isometries of certain modules in Euclidean $n$-space can be decomposed into a product of at most $n$ coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consisting of free modules with edges being classical matrix…
Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…
We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature.…
Composition principles for reduced moduli are extended to the case of domains in the $n$-dimensional Euclidean space, $n>2$. As a consequence analogues of extremal decomposition theorems of Kufarev, Dubinin and Kirillova in the planer case…
This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic structure of arc complexes.
The Dedekind-Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the…
We show that the deformation theory of a perfect complex and that of its determinant are related by the trace map, in a general setting of sheaves on a site. The key technical step, in passing from the setting of modules over a ring where…
We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C=R, this recovers the standard projective dimension. We show that three natural definitions of finite C-projective dimension…