Let k be a field. For each finite group G and two-cocyle f in Z 2(G,kx) (with trivial action), one can form the twisted group algebra kf G = ⊕σ∈G kxσ where xσxτ = f(σ, τ)xστ for all σ, τ ∈ G. Our main result is a short list of p-groups containing all the p-groups G for which there is a field k and a cocycle such that the resulting twisted group algebra is a k-central division algebra. We also complete the proof (presented in all but one case in a previous paper by Aljadeff and Halle) that every k-central division algebra that is a twisted group algebra is isomorphic to a tensor product of cyclic algebras.
|Number of pages||19|
|Journal||Israel Journal of Mathematics|
|State||Published - 2005|