This is an introduction to non-commutative geometry, with special emphasis on those cases
where the structure algebra, which defines the geometry, is an algebra of matrices over the …

We develop the formalism for noncommutative differential geometry and Riemmannian
geometry to take full account of the∗-algebra structure on the (possibly noncommutative) …

We analyze properties of a family of finite-matrix spaces obtained by a truncation of the
Heisenberg algebra and we show that it has a three-dimensional, noncommutative and …

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 construct new examples of left bialgebroids and Hopf algebroids, arising from
noncommutative geometry. Given a first order differential calculus $\Omega $ on an algebra …

We study geodesics in noncommutative geometry by means of bimodule connections and
completely positive maps using the Kasparov, Stinespring, Gel'fand, Naĭmark & Segal …

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 …

We consider differential operators over a noncommutative algebra A generated by vector
fields. These are shown to form a unital associative algebra of differential operators, and act …

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 …