A generalized Brauer construction and linear source modules

Boltje, Robert; Külshammer, Burkhard

doi:10.1090/S0002-9947-00-02530-7

A generalized Brauer construction and linear source modules
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by Robert Boltje and Burkhard Külshammer PDF

Trans. Amer. Math. Soc. 352 (2000), 3411-3428 Request permission

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

D. J. Benson, Representations and cohomology. I, Cambridge Studies in Advanced Mathematics, vol. 30, Cambridge University Press, Cambridge, 1991. Basic representation theory of finite groups and associative algebras. MR 1110581
Robert Boltje, A general theory of canonical induction formulae, J. Algebra 206 (1998), no. 1, 293–343. MR 1637292, DOI 10.1006/jabr.1998.7419
Robert Boltje, Linear source modules and trivial source modules, Group representations: cohomology, group actions and topology (Seattle, WA, 1996) Proc. Sympos. Pure Math., vol. 63, Amer. Math. Soc., Providence, RI, 1998, pp. 7–30. MR 1603127, DOI 10.1090/pspum/063/1603127
Michel Broué, On Scott modules and $p$-permutation modules: an approach through the Brauer morphism, Proc. Amer. Math. Soc. 93 (1985), no. 3, 401–408. MR 773988, DOI 10.1090/S0002-9939-1985-0773988-9
Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. I, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981. With applications to finite groups and orders. MR 632548
Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. II, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. With applications to finite groups and orders; A Wiley-Interscience Publication. MR 892316
J. A. Green, On the indecomposable representations of a finite group, Math. Z. 70 (1958/59), 430–445. MR 131454, DOI 10.1007/BF01558601
Jacques Thévenaz, $G$-algebras and modular representation theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. Oxford Science Publications. MR 1365077