Definition:Group Algebra
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Definition
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 $G$.
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