相关论文: Category of Noncommutative CW Complexes

Let $X$ be a simply connected path connected topological space which is formal in the sense of rational homotopy theory. Let $Y=X\cup_\alpha\mathbb{D}^{n}$ where $\alpha:\mathbb{S}^{n-1}\to X$ is a non-torsion element. Then we obtain a…

After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…

Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.

Real Bruhat cells give an important and well studied stratification of such spaces as $GL_{n+1}$, $Flag_{n+1} = SL_{n+1}/B$, $SO_{n+1}$ and $Spin_{n+1}$. We study the intersections of a top dimensional cell with another cell (for another…

Central to the theory of special cube complexes is Haglund and Wise's construction of the canonical completion and retraction, which enables one to build finite covers of special cube complexes in a highly controlled manner. In this paper…

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…

The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological…

The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in…

We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated…

Application of the noncommutative geometry to several physical models is considered.

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…

We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…

Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…

Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…

The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational CW-complex…

We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove that the totally nonnegative part of the Peterson variety is…

Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call…