\begin{definition}[Definition:Group Algebra]
Let $\struct {k, + ,\circ}$ be a field.
Let $\struct {G, *}$ be a finite group.
Then the '''group algebra''' $k G$ or $k \sqbrk G$ is the set of all formal sums:
:$\ds \sum_{g \mathop \in G} \alpha_g g : \alpha_g \in k$
That is, $k \sqbrk G$ is the free vector space over $k$ with basis $G$.
Category:Definitions/Abstract Algebra
\end{definition}