Theorem 3

Let $\mathscr{E}= (\Gamma , \iota , \pi )$ be a $\tau$-extension of G by $L^*$. The algebra $\mathbf{A}[\mathscr{E}; L]$ is central simple and of degree $n^2$ over K. Moreover, the canonical homomorphism $u$ from L to $\mathbf{A}[\mathscr{E}; L]$ is an isomorphism from L to a maximal commutative subalgebra of $\mathbf{A}[\mathscr{E}; L]$.