Related papers: A New Class of Two-Dimensional Noncommutative Spac…

We present non-perturbative results for U(1) gauge theory in spaces, which include a non-commutative plane. In contrast to the commutative space, such gauge theories involve a Yang-Mills term, and the Wilson loop is complex on the…

We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have…

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…

We develop a theory of non-relativistic bosons in two spatial dimensions with a weak short range attractive interaction. In the limit as the range of the interaction becomes small, there is an ultra-violet divergence in the problem. We…

Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which…

A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…

Two-sided conformally recurrent 4-dimensional self-dual spaces are considered. It is shown that such spaces are equipped with nonexpanding congruences of null strings. The general structure of weak nonexpanding hyperheavenly spaces is…

We discuss the model robustness of the infinite two-dimensional square grid with respect to symmetry breakings due to the presence of defects, that is, lacks of finitely or infinitely many edges. Precisely, we study how these topological…

Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

Here we construct a map from the algebra of fields in two-dimensional noncommutative of U(1) Yang-Mills fields interacting with Kaluza-Klein scalars to a D-dimensional one, as a solution in the two-dimensional model. This proves the…

We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.

Let \pi: Y -> X be a crepant projective resolution of an affine symplectic variety X with a good C^*-action. We interpret the second cohomology H^2(Y, C) in two ways. First, H^2(Y, C) is the Picard group of Y tensorised with C. By the ample…

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…

We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position…

This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…