The group algebra 
of a group 
is a vector space
 |
of finite formal sums of elements of 
, with multiplication
defined by 
, the group
operation. It is an example of a group ring.
For example, when the group is the symmetric group on three letters, 
,
the group ring 
is a six-dimensional algebra.
With permutation products
composed from left to right, an example of the product
of elements is
 |
Left unital CG-modules correspond to group representations of 
over the complex numbers.
When 
is a finite
group then 
is a finite-dimensional algebra.
