THE BRAIDED HEISENBERG-GROUP

The braided groups and braided matrices B(R) for the solution R of the Yang-Baxter equation associated to the quantum Heisenberg group are c omputed. It is also shown that a particular extension of the quantum H eisenberg group is dual to the Heisenberg universal enveloping algebra U(q)(h), and this result is used to derive an action of U(q)(h) on th e braided groups. The various covariance properties are then demonstra ted using the braided Heisenberg group as an explicit example. In addi tion, the braided Heisenberg group is found to be self-dual. Finally, a physical application to a system of n braided harmonic oscillators i s discussed. An isomorphism is found between the n-fold braided and un braided tensor products, and the usual ''free'' time evolution is show n to be equivalent to an action of a primitive generator of U(q)(h) on the braided tensor product.