Journal of Mathematical Chemistry

, Volume 54, Issue 2, pp 552–558 | Cite as

On the algebraic structure of central molecular chirality

Original Paper


We show that a group of 24 \(4\times 4\) permutation matrices that proved suitable for the study of chirality is a reducible representation of the group \({\mathcal {T}}_{d}\). 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 \(4\times 4\) permutation matrices is isomorphic to a group of \(3\times 3\) ones that form an irreducible representation of the elements of the group \({\mathcal {T}}_{d}\). We discuss the one-to-one correspondence between the two sets of matrices. A similar analysis can be carried out with the point group \({\mathcal {O}}\).


Chirality Permutation matrices Group theory  Homomorphism 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.División Química TeóricaINIFTA (UNLP, CCT La Plata-CONICET)La PlataArgentina

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