Commutative subalgebras of $\mathcal{U}(\mathfrak{q})$ of maximal transcendence degree

We prove that the enveloping algebra $\mathcal{U}(\mathfrak{q})$ of a finite-dimensional Lie algebra $\mathfrak{q}$ contains a commutative subalgebra of the maximal possible transcendence degree ($\operatorname{dim} \mathfrak{q} + \operatorname{ind} \mathfrak{q}) / 2$.

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This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — project number 404144169.

Received 26 July 2019

Accepted 13 March 2020

Published 2 June 2021