This lecture consists of two sections. In section 1 we consider the simplest version of aq-
deformed Heisenberg algebra as an example of a noncommutative structure. We first derive …

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 …

We apply one of the formalisms of noncommutative geometry to ℝ N q, the quantum space
covariant under the quantum group SO q (N). Over ℝ N q there are two SO q (N)-covariant …

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only
physical one. That approach restores Newton's original design of universal gravitation in the …

A bstract We introduce a model of a noncommutative BTZ black hole, obtained by
quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black …

We present classical groups SL⋆(2) and SU⋆(2) as well as classical Lie algebra sl 2⋆(C)
associated with a new associative multiplication on 2× 2 matrices. The idea of the new …

We propose a general procedure to construct noncommutative deformations of an
embedded submanifold M of R n determined by a set of smooth equations fa (x)= 0. We use …

The geometry of the q-deformed line is studied. A real differential calculus is introduced and
the associated algebra of forms represented on a Hilbert space. It is found that there is a …

We propose a general procedure to construct noncommutative deformations of an algebraic
submanifold M of ℝ n R^n, specializing the procedure G. Fiore, T. Weber, Twisted …

We show that the braided tensor product algebra A1 A2 of two module algebras A1, A2 of a
quasitriangular Hopf algebra H is isomorphic to the ordinary tensor product A1 A2, provided …