 Crossed-product algebra of a Galois extension (source code)

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= Crossed-product algebra of a Galois extension
{title2=$A(L,G,\phi)$}

For a finite Galois extension $L/k$, Galois group $G$, and normalized two-cocycle $\phi:G\times G\to L^\times$, the crossed-product algebra is
$$
A(L,G,\phi)=\bigoplus_{\sigma\in G}Lu_\sigma,
$$
with $u_\sigma a=\sigma(a)u_\sigma$ and $u_\sigma u_\tau=\phi(\sigma,\tau)u_{\sigma\tau}$. It is a central simple $k$-algebra split by $L$.

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