Multiple noncommutative tori and Hopf algebras

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.Comment: 18 pages; AMSLaTeX (major revision, the construction of dual rewritten using approach of multiplier Hopf algebras, references added

Quantum Stiefel Manifold And Double Cosets Of Quantum Unitary Group

Introduction. If a group G acts on a set S transitively on the right, then one can view S as G=K, where K is a subgroup of G. Thus a function on S can be considered as a function on G, invariant with respect to the right shifts by elements of K. It is especially interesting to consider bi-invariant functions on G since they can be identified with the functions on the set of G-orbits in S. If G is a locally compact group and K is its compact subgroup with Haar measures ¯G and ¯K respectively, then the set B ae L 1 (G; ¯G ) of all bi-invariant functions is an algebra with respect to the convolution and has a natural hypergroup structure related t