Related papers: Direct and inverse limits of normed modules
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of…
In this paper we define an orientation of a measured Gromov-Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
In this paper we generalize a shift theorem, which plays a key role in studying representations of FI$^m$, the product category of the category of finite sets and injections, and classify finitely generated injective FI$^m$-modules over a…
Numerical invariants of a minimal free resolution of a module $M$ over a regular local ring $(R,\n)$ can be studied by taking advantage of the rich literature on the graded case. The key is to fix suitable $\n$-stable filtrations ${\mathbb…
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N=2 superconformal field theory, we define the moduli space of N=2 super-Riemann spheres with oriented and ordered half-infinite tubes (or…
We investigate the category of discrete topological spaces, with emphasis on inverse systems of height $\omega_1$. Their inverse limits belong to the class of $P$-spaces, which allows us to explore dimensional types of these spaces.
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We use the $\eta$ invariants of spin$^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many non-diffeomorphic five dimensional manifolds for…
We classify the module categories over the double (possibly twisted) of a finite group.
We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…
An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having…
As the dual notion of projective modules over trusses, injective modules over trusses are introduced. The Schanuel Lemmas on projective and injective modules over trusses are exhibited in this paper.
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
We investigate extension of a measure to a very general set of undetermined structure. Structure may be imposed on this set in special cases
We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…
Let $R$ be a ring, and consider a left $R$-module given with two (generally infinite) direct sum decompositions, $A\oplus(\bigoplus_{i\in I} C_i)=M=B\oplus(\bigoplus_{j\in J} D_j),$ such that the submodules $A$ and $B$ and the $D_j$ are…