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arXiv · 2107.03111

Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications

Stjepan Meljanac·Zoran Škoda·Rina Štrajn
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Abstract

We introduce the generalized Heisenberg algebra appropriate for realizations of the $\mathfrak{gl}(n)$ algebra. Linear realizations of the $\mathfrak{gl}(n)$ algebra are presented and the corresponding star product, coproduct of momenta and twist are constructed. The dual realization and dual $\mathfrak{gl}(n)$ algebra are considered. Finally, we present a general realization of the $\mathfrak{gl}(n)$ algebra, the corresponding coproduct of momenta and two classes of twists. These results can be applied to physical theories on noncommutative spaces of the $\mathfrak{gl}(n)$ type.

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Stjepan Meljanac, Zoran Škoda, Rina Štrajn. 2021-07-07. Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications. https://doi.org/10.1016/s0034-4877(22)00013-1

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