A short historical review is made of some recent literature in the field of noncommutative
geometry, especially the efforts to add a gravitational field to noncommutative models of …

It is often thought that quantum groups provide the key to q-deforming the basic structures of
physics from the point of view of noncommutative geometry. If one considered a classical …

We describe noncommutative geometric aspects of twisted deformations, in particular of the
spheres of Connes and Landi and of Connes and Dubois Violette, by using the differential …

We consider integrable open spin chains related to the quantum affine algebras U q (o (3) ˆ)
and U q (A 2 (2))⁠. We discuss the symmetry algebras of these chains with the local C 3 …

A detailed study is made of the noncommutative geometry of R 3q, the quantum space
covariant under the quantum group SOq (3). For each of its two SOq (3)-covariant differential …

Let $ G $ be a simple complex factorizable Poisson algebraic group. Let $\mathcal U_\hbar
(\mathfrak g) $ be the corresponding quantum group. We study the $\mathcal U_\hbar …

Attention is focused on q-deformed quantum algebras with physical importance, ie Uq (su2),
Uq (so4) and q-deformed Lorentz algebra. The main concern of this article is to assemble …

Abstract GL q (N)-and SO q (N)-covariant deformations of the completely symmetric/
antisymmetric projectors with an arbitrary number of indices are explicitly constructed as …

The Euclidean Hopf algebra U4 (eN) dual of Fun (Ry> a SO,-r (N)) is constructed by
realizing it as a subalgebra of the differential algebra Diff (Rf) on the quantum Euclidean …

In this article we apply the systematic theory of braided geometry introduced during the last
few years by the author 1-5 to the problem of defining the totally antisymmetric tensor Eijk …