Non-commutative dual representation for quantum systems on Lie groups

Quantum Superalgebra Representations on Cohomology Groups of Non-commutative Bundles

Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of the quantum general linear supergroup. The right derived functors of this functor provides a form of D...

Lie theory for non-Lie groups

The class of locally compact groups admits a strong structure theory. This is due to the fact that—via approximation (projective limits)—important parts of the theory of Lie groups and Lie algebras carry over. This phenomenon becomes particularly striking if one assumes, in addition, that the groups under consideration are connected and of finite dimension. The aim of the present notes is to co...

Control Systems on Lie Groups

Non - commutative quantum dynamics ∗

We described a q-deformation of a quantum dynamics in one dimension. We prove that there exists only one essential deforamtion of quantum dynamics.

Algebraic methods: Lie groups, quantum groups

These notes concentrate on the paradigm of spherical functions on Riemannian symmetric spaces. This paradigm has led to the notion of special functions associated with root systems. The first sections deal with older work on the interaction between spherical functions on rank one symmetric spaces and special functions (q=1) in one variable. The (spectacular) developments in the higher rank case...