Extension of Characters from the Radical of a Connected Lie Group to a One-Dimensional Pure Pseudorepresentation of the Group Revisited

Investigations concerning the extension of characters on normal subgroups to one-dimensional pure pseudorepresentations of the enveloping groups are continued. We prove necessary and sufficient conditions that an ordinary unitary character on the radical of a connected Lie group admits an extension to a one-dimensional pure pseudorepresentation of the group and prove the uniqueness of this pure pseudorepresentation if it exists.

DOI 10.1134/S106192084010126