Related papers: Snyderspace
We analyze the structure of the algebra N of symmetric polynomials in non-commuting variables in so far as it relates to its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the…
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with…
Given a finite quiver, its double may be viewed as its non-commutative "cotangent" space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg constructed the non-commutative reduction of this space while…
We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting cases, can be rigorously constructed through the projective geometry description of Lorentzian, Galilean and Carrollian spaces with nonvanishing…
We show that the two-time physics model leads to a mechanical system with Dirac brackets consistent with the Snyder noncommutative space. An Euclidean version of this space is also obtained and it is shown that both spaces have a dual…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…
Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its…
By using graded (super) Lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. In this paper, we take a flat limit to obtain flat noncommutative superspace. We particularly consider $d=2$ and $d=4$…
We present generalisations of N-extended supersymmetry algebras in four dimensions, using Lorentz covariance and invariance under permutation of the N supercharges as selection criteria.
We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…
The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special…
The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.
An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently…
In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary…
We study the N=1/2 supersymmetric theory on noncommutative superspace which is a deformation of usual superspace. We consider deformed Wess-Zumino model as an example and show vanishing of vacuum energy, renormalization of superpotential…
We investigate the geode and some of its generalizations from the point of view on noncommutative symmetric functions.