Abstract
After a few illustrative examples, an attempt is made to give an algebraic definition of symmetry, suitable for generalizations which are usually described as colour symmetry. The wreath product of groups Perm(A) and Perm(M) over the setM is shown to be the most general group of those bijections of cartesian productM×A which are compatible with the concept of colour point. The recently introduced concepts ofP-,Q-,W p-, andW q-symmetries are discussed and it is shown thatQ-, andWq-symmetries can be, in a certain sense, reduced toP-, andW p-symmetries. The meaning of this reduction is briefly discussed for the case of spin groups.
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Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.
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Kopský, V. An algebraic study of contemporary symmetry concepts — Colour groups and related symmetries. Czech J Phys 32, 3–18 (1982). https://doi.org/10.1007/BF01597539
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DOI: https://doi.org/10.1007/BF01597539