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

Abstract

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

References in corpus (3)

• Crystals and monodromy of Bethe vectors
• Quantisation and nilpotent limits of Mishchenko-Fomenko subalgebras
• Poisson-commutative subalgebras of $S(\mathfrak{g})$ associated with involutions