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Transactions of the American Mathematical Society

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A generalized Brauer construction and linear source modules


Authors: Robert Boltje and Burkhard Külshammer
Journal: Trans. Amer. Math. Soc. 352 (2000), 3411-3428
MSC (2000): Primary 20C11, 20C20
DOI: https://doi.org/10.1090/S0002-9947-00-02530-7
Published electronically: March 21, 2000
MathSciNet review: 1694281
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Abstract: For a complete discrete valuation ring $\mathcal{O}$ with residue field $F$, a subgroup $H$ of a finite group $G$ and a homomorphism $\varphi: H \to \mathcal{O}^\times$, we define a functor $V \mapsto \overline{\overline{V}} (H,\varphi)$ from the category of $\mathcal{O} G$-modules to the category of $FN_G(H,\varphi)$-modules and investigate its behaviour with respect to linear source modules.


References [Enhancements On Off] (What's this?)

  • [Be] D. Benson: Representations and cohomology, vol. I. Cambridge University Press, Cambridge 1991. MR 92m:20005
  • [Bo96] R. Boltje: A general theory of canonical induction formulae. J. Algebra 206 (1998), 293-343. MR 99k:20013
  • [Bo98] R. Boltje: Linear source modules and trivial source modules. Proc. Sympos. Pure Math. 63 (1998), 7-30. MR 99d:20016
  • [Br] M. Broué: On Scott modules and $p$-permutation modules: An approach through the Brauer morphism. Proc. Amer. Math. Soc. 93 (1985), 401-408. MR 86d:20010
  • [CR81] C.W. Curtis, I. Reiner: Methods of representation theory, Vol. 1. J. Wiley & Sons, New York 1981. MR 82i:20001
  • [CR87] C.W. Curtis, I. Reiner: Methods of representation theory, Vol. 2. J. Wiley & Sons, New York 1987. MR 88f:20002
  • [Gr] J.A. Green: On the indecomposable representations of a finite group. Math. Zeitschr. 70 (1959), 430-445. MR 24:A1304
  • [Th] J. Thévenaz: $G$-algebras and modular representation theory. Oxford University Press 1995. MR 96j:20017

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Additional Information

Robert Boltje
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
Email: boltje@math.ucsc.edu

Burkhard Külshammer
Affiliation: Mathematisches Institut, Universität Jena, 07 740 Jena, Germany
Email: kuelshammer@uni-jena.de

DOI: https://doi.org/10.1090/S0002-9947-00-02530-7
Received by editor(s): April 28, 1998
Published electronically: March 21, 2000
Additional Notes: The first author’s research was supported by the DFG
Article copyright: © Copyright 2000 American Mathematical Society

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