Group theory in geometry
Date: Around 1995
I need to know something about group theory in relation to geometry, such
as: if the symmetry of an object can be described by a group G, what does
subgroup H in G mean in relation to the object? The center? Centralizer? A
normal subgroup? etc.
Maybe you could give me a reference to a book about this - level about post
Well, a reference chemists have used on this subject for many years is
Cotton's "Chemical Applications of Group Theory."
In the context of identifying the point group of an object, the elements of
the group correspond to rotations, reflections, inversions, etc. of the
object that leave the object's shape invariant. At least, this is what it
boils down to for molecules. I have probably skipped over 1000's of
mathematical subtleties which a real mathematician will hopefully fill in
hereafter . . . (?) But I think you will find Cotton's book of interest.
You can also see the relevant chapter in any general physical chemistry text
(example: Atkins' "Physical Chemistry").
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Update: June 2012