Mathematical Research Letters

Volume 28 (2021)

Number 3

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

Pages: 907 – 924



Oksana Yakimova (Institut für Mathematik, Friedrich-Schiller-Universität Jena, Germany)


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 ($\operatorname{dim} \mathfrak{q} + \operatorname{ind} \mathfrak{q}) / 2$.

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