Related papers: Twist for Snyder space
We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…
An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a…
We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from realizations are presented, as well as their…
We describe all finite-dimensional pointed Hopf algebras whose infinitesimal braiding is a fixed Yetter-Drinfeld module decomposed as the sum of two simple objects: a point and the one of transpositions of the symmetric group in three…
We consider the issue of statistics for identical particles or fields in kappa-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is…
We begin by considering the graded vector space with a basis consisting of rooted trees, graded by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively…
We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are defined on groupoids whose algebroid can be endowed with a…
The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat…
The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincar\'e symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading…
We consider a generalisation of the Majid's mirror product of a Hopf algebra H, when one of the components of the product is replaced by a twist. This leads to a new "twisted mirror product" construction for cocycle bicrossproduct Hopf…
We construct a Hopf algebra cocycle in the Yangian double $DY(SL_{2})$, conjugating Drinfeld's coproduct to the usual one. To do that, we factorize the twist between two ``opposite'' versions of Drinfeld's coproduct, introduced in earlier…
We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of…
We introduce natural binary set-theoretical products on the set of all $m$-Dyck paths, which led us to define a non-symmetric algebraic operad $\Dy^m$, described on the vector space spanned by $m$-Dyck paths. Our construction is closely…
Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module…
We construct two types of scalar field theory on Snyder space-time. The first one is based on the natural momenta addition inherent to the coset momentum space. This construction uncovers a non-associative deformation of the Poincar\'e…
In this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot theory and integrable systems. In particular we introduce the…
Using the Hopf fibration and starting from a four dimensional noncommutative Moyal plane, $R^2_{\theta}\times R^2_{\theta}$, we obtain a star-product for the noncommutative (fuzzy) $R^3_{\lambda}$ defined by…
In this paper, we consider the Reshetikhin-Turaev invariants of knots in the three-sphere obtained from a twisted Drinfeld double of a Hopf algebra, or equivalently, the relative Drinfeld center of the crossed product…
We describe quasi-Hopf twist deformations of flat closed string compactifications with non-geometric R-flux using a suitable cochain twist, and construct nonassociative deformations of fields and differential calculus. We report on our new…