We give a pedagogical introduction to the differential calculus on quantum groups by
stressing at all stages the connection with the classical case (q→ 1 limit). The Lie derivative …

We present a general method to deform the inhomogeneous algebras of the B n, C n, D n
type, and find the corresponding bicovariant differential calculus. The method is based on a …

We find two different q-generalizations of Yang-Mills theories. The corresponding
lagrangians are invariant under the q-analogue of infinitesimal gauge transformations. We …

We specify a set of relations between non-commuting matrix elements and their differentials,
defined in terms of an R-matrix satisfying the braid relation, which are uniquely determined …

The non-commutative differential calculus on the quantum groups SLq (N) is constructed.
The quantum external algebra proposed contains the same number of generators as in the …

We construct differential calculi on multiparametric quantum orthogonal planes in any
dimension N. These calculi are bicovariant under the action of the full inhomogeneous …

Under the assumptions that q is not a root of unity and that the differentials du ji of the matrix
entries span the left module of first order forms, we classify bicovariant differential calculi on …

A reformulation of the Itô calculus of stochastic differentials is presented in terms of a
differential calculus in the sense of noncommutative geometry (with an exterior derivative …

We study the foundations of the differential calculus in quantum geometry. The notions of
(differential) quantum space and cone are introduced. Generalizing a construction of Manin …

We consider the possible covariant external algebra structures for Cartan's 1-forms (Omega)
on GL q (N) and SL q (N). Our starting point is that the Omega realize an adjoint …