NDLI: Burnside Rings: Application to Molecules of Icosahedral Symmetry

Content Provider	Springer Nature Link
Author	Martínez Torres, Emilio
Copyright Year	2004
Abstract	The Burnside ring, B(G), of a group G is the set of isomorphism classes of orbits of G together with the operations of addition and product. The addition is defined as the disjoint union, and the product as the Cartesian product. This paper describes basic facts about this algebraic structure and develops some applications in chemistry, as the labelling of atoms in molecules of high symmetry and the construction of symmetry-adapted functions. For illustrating such applications, the concept of Burnside ring is applied to the icosahedral symmetry. Sets of points which are isomorphic to the orbits of the I group are described and the multiplication table of B({I}) is obtained from the table of marks. This multiplication table allows us to obtain an elegant labelling of the atoms of the buckminsterfullerene which is consistent with the icosahedral symmetry. Also, we obtain complete sets of symmetry-adapted functions for the buckminsterfullerene which span the Boyle and Parker's icosahedral representations.
Starting Page	105
Ending Page	117
Page Count	13
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	35
Issue Number	2
e-ISSN	15728897
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Math. Applications in Chemistry Physical Chemistry Theoretical and Computational Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

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