Related papers: A note on commutative and noncommutative Gurariy s…
In this paper we develop the theory of Artin-Wraith glueings for topological spaces. As an application, we show that some categories of compactifications of coarse spaces that agree with the coarse structures are invariant under coarse…
A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…
Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
We consider a conservative Markov semigroup on a semi-finite $W^*$-algebra. It is known that under some reasonable assumptions it is enough to determine a kind of differential structure on such a 'noncommutative space'. We construct an…
The goal of this paper is to define a notion of non-commutative Gelfand duality. Using techniques from derived algebraic geometry, we show that the category of rings is anti-equivalent to a subcategory of pre-ringed sites, inspired by…
Gravitational axial and chiral anomalies in a noncommutative space are examined through the explicit perturbative computation of one-loop diagrams in various dimensions. The analysis depend on how gravity is coupled to noncommutative matter…
This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.
We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…
I review my results about noncommutative gauge theories and about the relation of these theories to M(atrix) theory following my lecture on ICMP 2000.
We summarize the arguments that space and time are likely to be emergent notions; i.e. they are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts. Along the way we briefly review…
The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…
The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
In this paper we introduce non-commutative analogues for the quasi-Hamiltonian $G$-spaces introduced by Alekseev, Malkin and Meinrenken. We outline the connection with the non-commutative analogues of quasi-Poisson algebras which the author…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of…
In this paper, we construct a function which confirms the proper inclusion property of Morrey spaces, by using a relation between a class of functions in Morrey spaces and discrete Morrey spaces. Our particular function is simpler than…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
In this paper we consider two kinds of noncommutative space-time commutation relations in two-dimensional configuration space and feature the absolute value of the minimal length from the generalized uncertainty relations associated to the…