an:07222095
Zbl 1443.81044
Meljanac, Stjepan; Martini??-Bila??, Tea; Kre??i??-Juri??, Sa??a
Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz, and Poincar?? algebras and their dual extensions
EN
J. Math. Phys. 61, No. 5, 051705, 13 p. (2020).
00450987
2020
j
81R60 33C65 14D15 11R60 22E43
Summary: We introduce the generalized Heisenberg algebra \(\mathcal{H}_n\) and construct realizations of the orthogonal and Lorentz algebras by a formal power series in a semicompletion of \(\mathcal{H}_n\). 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 \(\mathcal{H}_n\). Furthermore, we show that by extending the generalized Heisenberg algebra \(\mathcal{H}_n\), one can also obtain realizations of the Poincar?? algebra and its extension by quantum angles.
{\copyright 2020 American Institute of Physics}