Related papers: Projective space of a C*-module

Let A be an affine algebra over the field of real numbers of dimension d. Let f \in A be an element not belonging to any real maximal ideal of A. Let P be a projective A-module of rank \geq d-1. Let (a,p) \in A_f \oplus P_f be a unimodular…

Given a compact connected Riemann surface $X$ equipped with an antiholomorphic involution $\tau$, we consider the projective structures on $X$ satisfying a compatibility condition with respect to $\tau$. For a projective structure $P$ on…

We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…

In this paper, we first show that for an acyclic gentle algebra A, the irreducible components of any moduli space of A-modules are products of projective spaces. Next, we show that the nice geometry of the moduli spaces of modules of an…

Let $R$ be a Noetherian ring of dimension $d$ and $A$ be a graded $R$-subalgebra of $R[X,1/X]$. Let $P$ be a projective module over $A$ of rank $r \geq \max\{d+1,2\}$ and $\v=(a,p)$ be a unimodular element of $A \oplus P$. We find an…

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…

Given a compact manifold X, the set of simple manifold structures on X x \Delta^k relative to the boundary can be viewed as the k-th homotopy group of a space \S^s (X). This space is called the block structure space of X. We study the block…

Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and <, >_A : H \times H \to C the bounded sesquilinear form induced by a selfadjoint A in L(H), < \xi, \eta >_A = < A \xi, \eta >, \xi, \eta in H. Given T in…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

Synthetic algebraic geometry is a new approach to algebraic geometry. It consists in using homotopy type theory extended with three axioms, together with the interpretation of these in a higher version of the Zariski topos, in order to do…

Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…

A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural…

We study the moduli space of A-infinity structures on a topological space as well as the moduli space of A-infinity-ring structures on a fixed module spectrum. In each case we show that the moduli space sits in a homotopy fiber sequence in…

We study the structure of the $0$-Schur algebra $S_0(n, r)$ following the geometric construction of $S_0(n, r)$ by Jensen and Su \cite{JS}. The main results are the construction and classification of indecomposable projective modules. In…

Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H^*(LX_hT; Z/p) as a module over H^*(BT; Z/p) when X=CP^r for any positive integer…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type <X, 0, ', .> where 0 is a constant, ' is unary and . is…

In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms…

A pure topological characterization of primitive ideal spaces of separable nuclear C*-algebras is given. We show that a $T_0$-space $X$ is a primitive ideal space of a separable nuclear C*-algebra $A$ if and only if $X$ is point-complete…