Group-Algebras

For a field $k$ and finite group $G=\{g_1,\dots ,g_n\}$, the group-algebra $k[G]$ consists of linear combinations of the elements of $G$. In other words, $k[G]=\left\{{\sum }_{i=1}^n{c}_i{g}_i|c_i\in k\right\}.$