## When is a crossed-product algebra a division algebra?

Let L/K be a finite Galois extension with Galois group G. For every 2-cocycle γ of G with values in L× there is the crossed-product K-algebra S(L,G,γ)=⨁g∈GLeg with the multiplication (μeg)⋅(λeh)=μg(λ)γ(g,h)egh for all λ,μ∈L. The K-algebra S(L,G,γ) is a central simple K-algebra. In fact, the isomorphism class of S(L,G,γ) only depends on the cohomology class … Read more