相关论文: Spin and Statistics on the Groenewold-Moyal Plane:…

Fourier-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position…

Dynamical symmetries of Born-Infeld theory can be absorbed into the spacetime geometry, giving rise to relativistic kinematics with an additional invariant acceleration scale. The standard Poincare group P is thereby enhanced to its…

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge…

Due to Rentschler, Miyanishi and Kojima, the invariant ring for a ${\bf G}_a$-action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we give a new short proof for this result using the automorphism…

The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under…

We note a remarkable similarity between the discretized Weyl-orbit functions and affine modular data associated with Wess-Zumino-Novikov-Witten (WZNW) conformal field theories. Known properties of the modular data are exploited here to…

Twisted generalized Weyl algebras (TGWAs) $A(R,\sigma,t)$ are defined over a base ring $R$ by parameters $\sigma$ and $t$, where $\sigma$ is an $n$-tuple of automorphisms, and $t$ is an $n$-tuple of elements in the center of $R$. We show…

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the $q\to 1$ scaling limit of the braided adjoint action or $R$-commutator of $q$-Minkowski space on itself. We also describe the…

Let $H$ be a Hopf algebra over a field $K$ of characteristic $0$ and let $A$ be a bialgebra or Hopf algebra such that $H$ is isomorphic to a sub-Hopf algebra of $A$ and there is an $H$-bilinear coalgebra projection $\pi$ from $A$ to $H$…

We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This…

The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…

Let $f:\mathbb{T}\to\mathbb{R}$ be a Morse function of class $C^2$ with exactly two critical points, let $\omega\in\mathbb{T}$ be Diophantine, and let $\lambda>0$ be sufficiently large (depending on $f$ and $\omega$). For any value of the…

The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform…

Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant…

For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to…

Minkowski space, conformal group, compactification, conformal infinity, conformal inversion, light cone at infinity, SU(2,2), SO(4,2), Hodge star operator, Clifford algebra, spinors, twistors, antilinear operators, exterior algebra,…

Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…

We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…

We introduce a unital associative algebra A over degenerate CP^1. We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions. Thereby we can regard A as a smooth degeneration limit of the…

The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W_\infty. q-star products and q-Moyal brackets corresponding to these algebras are…