Related papers: Notes on Super Projective Modules
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results of arXiv:1706.01354, we study an explicit example of non-projected and…
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of…
Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a complex projective curve and constructed a projective moduli space of such objects. We generalize Ramanathan's notion and…
We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
We give a complete classification of isomorphism classes of finitely generated projective modules, or equivalently, unitary equivalence classes of projections, over the C*-algebra $C\left( \mathbb{S}_{q}^{2n+1}\right) $ of the quantum…
Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…
In this paper we will study the projetivity of various natural modules associated to operator Segal algebras of the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules…
In this note we give a complete description of all the hyperplane section of the projective bundle associated to the tangent bundle of $\mathbb{P}^2$ under its natural embedding in $\mathbb{P}^7.$ As an application one obtains a description…
Assuming Hartshorne's conjecture on complete intersections, we classify projective bundles over projective spaces which has a smooth blow up structure over another projective space. Under some assumptions, we also classify projective…
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…
This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring $R$, we present a characterization of indecomposable projective $R$-modules and describe a…
A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…