Four lines in space (Q1021354)

The author defines a cross-ratio-like invariant for four lines in general position in three-di\-men\-sion\-al projective space, such that two sets of four lines are equivalent under a linear transformation if and only if the invariants associated to the two sets are equal. This invariant is used to investigate representations of the infinite dihedral group (previously studied by \textit{S. D. Berman} and \textit{K. Buzási} [Publ. Math. 28, 173--187 (1981; Zbl 0485.20007)] and by \textit{D. Ž. Đoković} [J. Algebra 100, 214--223 (1986; Zbl 0593.20009)]) in dimension 4, and to provide a computational tool to determine whether two given representations are equivalent or not.