Related papers: Non-commutative crepant resolutions: scenes from c…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…
In this paper, we study noncommutative surface singularities arising from orders. The singularities we study are mild in the sense that they have finite representation type or, equivalently, are log terminal in the sense of the Mori minimal…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…
This paper presents a new approach to studying nonlinear resolvents of holomorphically accretive mappings on the open unit ball of a complex Banach space. We establish a distortion theorem and apply it to address problems in geometric…
Let $L$ be a finite-dimensional non-abelian Lie algebra with the center $Z(L)$. In this paper, we define a non-commuting graph associated with $L$ as the graph whose vertex set is the projective space of the quotient algebra $L/Z(L)$, and…
The purpose of this paper is to construct a crepant resolution of quotient singularities by trihedral groups ( finite subgroups of SL(3,C) of certain type ), and prove that each Euler number of the minimal model is equal to the number of…
We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a…
Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the derived categories of perverse sheaves, and nowadays become very powerful in understanding relationship among three algebraic, geometric or topological…
This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and…
We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves…
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…
We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any…
We study non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary representations of a compact group. Our main goal is searching for orthogonal projections which are anticliques…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the…
To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…
In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on…