Projective bases of division algebras and groups of central type |
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Authors: | Email author" target="_blank">Eli?AljadeffEmail author Darrell?Haile Michael?Natapov |
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Institution: | (1) Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel;(2) Department of Mathematics, Indiana University, 47405 Bloomington, IN, USA;(3) Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | Letk be a field. For each finite groupG and two-cocylef inZ
2
(G, k
x
) (with trivial action), one can form the twisted group algebra
wherex
σ
x
τ
=f(σ,τ)x
στ
for all σ, τ∃G. Our main result is a short list ofp-groups containing all thep-groupsG for which there is a fieldk and a cocycle such that the resulting twisted group algebra is ak-central division algebra. We also complete the proof (presented in all but one case in a previous paper by Aljadeff and Haile)
that everyk-central division algebra that is a twisted group algebra is isomorphic to a tensor product of cyclic algebras. |
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Keywords: | |
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