Abstract
We introduce the generalized Heisenberg algebra Hn and construct realizations of the orthogonal and Lorentz algebras by a formal power series in a semicompletion of Hn. The obtained realizations are given in terms of the generating function for the Bernoulli numbers. We also introduce an extension of the orthogonal and Lorentz algebras by quantum angles and study realizations of the extended algebras in Hn. Furthermore, we show that by extending the generalized Heisenberg algebra Hn, one can also obtain realizations of the Poincaré algebra and its extension by quantum angles.
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