CG
Given a group G, the algebra CG is a vector space
| CG={suma_ig_i|a_i in C,g_i in G} |
of finite sums of elements of G, with multiplication defined by g·h=gh, the group operation. It is an example of a group ring.
For example, when the group is the symmetric group on three letters, S_3, the group ring CS_3 is a six-dimensional algebra. An example of the product of elements is
Modules over CG correspond to complex group representations of G. When G is a finite group then CG is a finite-dimensional algebra.
See also
Algebra, Group, Group Representation, Group Ring, Permutation, RingThis entry contributed by Todd Rowland
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Rowland, Todd. "CG." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CG.html