To the Segal chronometric theory

The author expounds or proves some results connected with Segal's chronometric theory. He gives short proofs of results about linear representation of the group of nondegenerate complex (2$\times$2)-matrices on the Minkowski space-time and on the universal covering of the Lie group of unitary (2$\times$2)-matrices, i.e., on the Einstein Universe, as well as about the Cayley transform of Lie algebras of Lie groups of unitary matrices into these groups. In comparison with the structure of conformal infinity for the Minkowski space, the structure of the set of unitary (2$\times$2)-matrices, which do not admit the Cayley transform, is found. Some problems are suggested.