Abstract
So far our discussion has been non-mathematical. Ignoring mathematics, however, does not make things necessarily easier. Group theory is the mathematical apparatus for describing symmetry operations. It facilitates the understanding and the use of symmetries. It may not even be possible to successfully attack some complex problems without the use of group theory. Besides, groups are fascinating.
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Notes
- 1.
Shortly, we shall use a wide range of operands related to molecular structure.
- 2.
In linear algebra this is usually called trace.
- 3.
Antisymmetry will be discussed in the next Section.
- 4.
§Not to be confused with the symbol of the identity operation, which is also E.
- 5.
The Russian word “perestroika” means restructuring.
- 6.
Here and hereafter the short expression “character of R” stands for the character of the matrix corresponding to operation R, in accordance with our previous discussion.
- 7.
Unless, of course, identical atoms are distinguished by labels as, e.g., in Figs. 4-2 and 4-3.
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Ibid.
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Hargittai, M., Hargittai, I. (2009). Helpful Mathematical Tools. In: Symmetry through the Eyes of a Chemist. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5628-4_4
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