Solvable Lie groups with factor regular representations (Q6606753)

The paper deals essentially with the notion of factor regular representations. It begins with a brief introduction on some generalities on representation theory of discrete groups, factor representations... Next, in Section 2, one gives some very basic notions which will be useful for the remainder of the paper. The main results in this paper concerning characterization of solvable Lie groups whose regular representation is a factor representation are in Section 4. In Section 5, one gives a family of examples of Lie groups which show that every value \(\geq 3 \) of the codimension of the nilradical can be realized concretely, but the value \(2\) still remains elusive.\N\NFor the entire collection see [Zbl 1531.53004].