Irreducible representations of infinite-dimensional transformation groups and Lie algebras. I (Q1893832)

In the paper there are given some results on the irreducibility and inequivalence of representations of infinite dimensional Lie algebras, related to transformation groups; among others there is a generalization of a classical result of Burnside. Applications to the study of the Dirac quantization problem of representing a Lie algebra of functions on a symplectic manifold are given.