The quantum Euclidean spheres, S q , are (noncommutative) homogeneous spaces of quantum orthogonal groups, SOq(N). The ∗-algebra A(S q ) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and ...

We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics. Talk given at the Conference on Fundamental Problems in Quantum Theory Baltimore, June 18–22, 1994 Consider a dilute gas of hard spheres in a box with hard walls. Give the spheres some arbitrary i...