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In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct…
We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…
A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first order differential calculus on such a…
A quasi-projection pair consists of two operators $P$ and $Q$ acting on a Hilbert $C^*$-module $H$, where $P$ is a projection and $Q$ is an idempotent satisfying $Q^*=(2P-I)Q(2P-I)$, in which $Q^*$ denotes the adjoint operator of $Q$, and…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
In the last few years, Lopez-Permouth and several collaborators have introduced a new approach in the study of the classical projectivity, injectivity and flatness of modules. This way, they introduced subprojectivity domains of modules as…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class…
Projective modules are a link between geometry and algebra as established by the theorem of Serre-Swan. In this paper, we define the super analog of projective modules and explore this link in the case of some particular super geometric…
Slicing a module into semisimple ones is useful to study modules. Loewy structures provide a means of doing so. To establish the Loewy structures of projective modules over a finite dimensional symmetric algebra over a field $F$, the…
We present an extension of Naimark's duality principle which states that complete systems in a Hilbert space are projections of $\omega$-linearly independent systems of elements of an ambient Hilbert space. This result is presented in the…
We develop the basic properties of $R^{(2)}$-modules, introduce the concept of zero divisor manifolds, construct projective $R^{(2)}$-space which generalizes the real projective space, and initiate the study of the counterpart of symplectic…
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
In this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative…
We study intersections of projective convex sets in the sense of Steinitz. In a projective space, an intersection of a nonempty family of convex sets splits into multiple connected components each of which is a convex set. Hence, such an…
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…
For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…
We introduce a quotient of the affine Temperley-Lieb category that encodes all weight-preserving linear maps between finite-dimensional sl(2)-representations. We study the diagrammatic idempotents that correspond to projections onto…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…