Projective bases of division algebras and groups of central type

Eli Aljadeff*, Darrell Haile, Michael Natapov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)317-335
Number of pages19
JournalIsrael Journal of Mathematics
Volume146
DOIs
StatePublished - 2005
Externally publishedYes

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