Algebra VIII: Representations of Finite-dimensional AlgebrasАлексей Иванович Кострикин, Игорь Ростиславович Шафаревич |
Contents
Foreword | 2 |
Matrix Problems | 4 |
Algebras Modules and Categories | 15 |
Copyright | |
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a₁ a₂ admits aggregate algebraically closed field antichain arrows associated b₁ b₂ bijection bimodule Bongartz c₁ c₂ coherent connected component contains defined denote derived categories dimension dimension-function distributive spectroid dualizing endomorphism epimorphism equivalent exact sequence exact structure Example extended Dynkin finite poset finitely presented finitely represented follows full subcategory functor F Gabriel gives rise hence ideal idempotents identified implies indecomposable modules induces injective invertible isoclasses of indecomposables isomorphic k-category left module Lemma linear M-spaces maps matrix problem minimal Mod k(P morphism non-zero objects obtain orbits P₁ pairs penny-farthing pointwise finite poset positive roots projective Proof quadratic form quiver Q quotient ray-category resp S-modules satisfies Sect Shafarevich simple modules space spectroid split sequence submodule subset summand suppose surjective Theorem V₁ vector vertex vertices weakly positive X₁