相关论文: A non-commutative BGG correspondence

This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…

We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.

We prove a BGG type reciprocity law for the category of finite dimensional modules over algebraic supergroups satisfying certain conditions. The equivalent of a standard module in this case is a virtual module called Euler characteristic…

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

The quasi-Newton equation is the very basis of a variety of the quasi-Newton methods. By using a relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix. presented recently by the present author, we…

Let E = K< y_1, ..., y_n > be the exterior algebra. The ``(cohomological) distinguished pairs" of a graded E-module M describe the growth of a minimal graded injective resolution of M. Roemer gave a duality theorem between the distinguished…

Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field (see arXiv:0802.0791 [math-ph]), we introduce models for non-commutative U(1) gauge fields along the same lines. More…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our…

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

The bulk-boundary correspondence (BBC), i.e. the direct relation between bulk topological invariants defined for infinite periodic systems and the occurrence of protected zero-energy surface states in finite samples, is a ubiquitous and…

We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…

Let ${p > 2}$ be an odd prime and ${G = SL_2(\mathbb{F}_p)}$. Denote the subgroup of upper triangular matrices as $B$. Finally, let ${\mathbb{F}}$ be an algebraically closed field of characteristic ${p}$. The Green correspondence gives a…

A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the…

We give a general approach to infinite dimensional non-Gaussian analysis which generalizes the work \cite{KSWY95}. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that…

The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…

We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…

We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. We showed previously that in certain gauges some cohomology classes of the gauge-fixed BRST differential do not correspond to gauge invariant…

We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.

Addition formulae of trigonometric and elliptic functions are used to generate B\"acklund transformations together with their connecting quadrilateral equations. As a result we obtain periodic solutions for a number of multidimensionally…