2004
DOI: 10.1515/jgth.2004.004
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On representations of twisted group rings

Abstract: We generalize certain parts of the theory of group rings to the twisted case. Let G be a finite group acting (possibly trivially) on a field L of characteristic coprime to the order of the kernel of this operation. Let K J L be the fixed field of this operation and let S be a discrete valuation ring with field of fractions K, with maximal ideal generated by p and with integral closure T in L. We compute the colength of T o G in a maximal order in L o G. In the case when S=pS is finite, we compute the S=pS-dime… Show more

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Cited by 3 publications
(3 citation statements)
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“…is semi-simple, see e.g., [Kün04,Lemma 1.3]. We may therefore choose compatible splittings Ind((W 1 ) ∨ L ) → ∩m i and Ind((W 2 ) ∨ L ) → ∩m i to the horizontal arrows.…”
Section: Documenta Mathematica 20 (2015) 269-332mentioning
confidence: 99%
“…is semi-simple, see e.g., [Kün04,Lemma 1.3]. We may therefore choose compatible splittings Ind((W 1 ) ∨ L ) → ∩m i and Ind((W 2 ) ∨ L ) → ∩m i to the horizontal arrows.…”
Section: Documenta Mathematica 20 (2015) 269-332mentioning
confidence: 99%
“…We can generalise this situation and still get similar results. For example, if G is a finite group with a given epimorphism π : G −→ G, then ℓ♯ G is semi-simple provided that p ∤ | ker π|, see [10]. In fact the unicursal Hopf algebroid F ⊗ Fp F(θ 0 ) of (5.2) is dual to…”
Section: Lubin-tate Spectra and Their Hopf Algebroidsmentioning
confidence: 99%
“…They were discussed for an audience of topologists in [1], and their duals as Hopf algebroids were discussed. For a recent reference on their modules see [10]. Here we focus on the special case of Galois extensions of fields, which is closely related to the unicursal Hopf algebroids.…”
Section: Unicursal Hopf Algebroidsmentioning
confidence: 99%