On the algebraic structure of central molecular chirality

Abstract

We show that a group of 24 4×4 permutation matrices that proved suitable for the study of chirality is a reducible representation of the group Td . Consequently, all the mathematical properties of the former matrices can be easily inferred from the table of characters of the latter group. We also show that the group of 4×4 permutation matrices is isomorphic to a group of 3×3 ones that form an irreducible representation of the elements of the group Td . We discuss the one-to-one correspondence between the two sets of matrices. A similar analysis can be carried out with the point group O.