Projective bases of division algebras and groups of central type

TY - JOUR

T1 - Projective bases of division algebras and groups of central type

AU - Aljadeff, Eli

AU - Haile, Darrell

AU - Natapov, Michael

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=18444365563&partnerID=8YFLogxK

U2 - 10.1007/BF02773539

DO - 10.1007/BF02773539

M3 - 文章

AN - SCOPUS:18444365563

SN - 0021-2172

VL - 146

SP - 317

EP - 335

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -