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arXiv · 1409.8188

Lie algebra type noncommutative phase spaces are Hopf algebroids

Stjepan Meljanac·Zoran Škoda·Martina Stojić
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Abstract

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way, therefore obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.

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Stjepan Meljanac, Zoran Škoda, Martina Stojić. 2016-12-12. Lie algebra type noncommutative phase spaces are Hopf algebroids. https://doi.org/10.1007/s11005-016-0908-9

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