Related papers: Projective real calculi over matrix algebras
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…
We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively…
We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…
Let D^n be the closed unit polydisk in C^n. Consider the ring C_r of complex-valued continuous functions on D^n that are real symmetric, that is, f(z)=(f(z^*))^* for all z in D^n. It is shown that C_r is projective free, that is, finitely…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
In order to investigate to what extent the calculus of classical (pseudo-)Riemannian manifolds can be extended to a noncommutative setting, we introduce pseudo-Riemannian calculi of modules over noncommutative algebras. In this framework,…
In this paper, we introduce a new notion of representation for a locally convex partial *-algebraic module as a concrete space of maps. This is a continuation of our systematic study of locally convex partial *-algebraic modules, which are…
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the…
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We introduce the notion of the moduli stack of relations of a quiver. When the quiver with relations is derived-equivalent to an algebraic variety, the corresponding compact moduli scheme can be viewed as a compact moduli of noncommutative…
The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over…
For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also…
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…
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…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…