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Generalized Fixpoint Algebras
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abelian group assume basis element BK(P Brauer construction Brauer kernel called capped endo-monomial OP-module capped endo-permutation Chapter class of capped conjugation crossed product Dade's theorem decomposition 4.2.1.a defined denote direct sum direct summand isomorphic discrete valuation ring embedding endo endo-monomial modules endo-permutation modules endo-trivial Endo(M endomorphism algebra equivalence classes equivalence relation field F finite group fix a decomposition g G G G-action G-graded ring group homomorphism hence i?G-module idempotents indecomposable direct summand indecomposable endo-monomial OP-module induced interior G-algebras ip G P Lemma Lemma Let linear character monomial Dade group monomial Dade P-algebra monomial modules monomial OP-module non-abelian OP-isomorphism OP-module with vertex p-group p-i p-i permutation module pointed groups projective-free Proof Puig reduction modulo RG-module Robert Boltje root of unity short exact sequence subgroup H subgroup of G summand with vertex surjective Thevenaz trace map twisted group algebra unique vertex Q VF(P Vr(P write