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The Braided Heisenberg Group
We compute the braided groups and braided matrices for the solution
of the Yang-Baxter equation associated to the quantum Heisenberg group. We
also show that a particular extension of the quantum Heisenberg group is dual
to the Heisenberg universal enveloping algebra , and use this result
to derive an action of on the braided groups. We then demonstrate
the various covariance properties using the braided Heisenberg group as an
explicit example. In addition, the braided Heisenberg group is found to be
self-dual. Finally, we discuss a physical application to a system of n braided
harmonic oscillators. An isomorphism is found between the n-fold braided and
unbraided tensor products, and the usual `free' time evolution is shown to be
equivalent to an action of a primitive generator of on the braided
tensor product.Comment: 33 page
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