Commutativity of missing label operators in terms of Berezin brackets

Abstract

We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement of missing label operators for reduction chains in the missing label problem can be solved analytically.

References in corpus (3)

• Internal labelling operators and contractions of Lie algebras
• Non-solvable contractions of semisimple Lie algebras in low dimension
• Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras

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