Quantum fields on noncommutative spacetimes: theory and phenomenology.
Binary operations in classical and quantum mechanics
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply properties which are usually additionally required.
Tensor fields defining a tangent bundle structure
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
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