On the quantum argument shift method
Yasushi Ikeda, Alexander Ivanovich Molev, Georgy Sharygin · Communications in Algebra · 2025
In a recent work by two of us the argument shift method was extended from the symmetric algebra S(g) of the general linear Lie algebra g to the universal enveloping algebra U(g). We show in this paper that some features of this “quantum argument shift method” can be applied to the remaining classical matrix Lie algebras g. We prove that a single application of the quasi-derivation to central elements of U(g) yields elements of the corresponding quantum Mishchenko–Fomenko subalgebra. We show that generators of this subalgebra can be obtained by iterated application of the quasi-derivation to generators of the center of U(g).