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Realizations of valued graphs and
The Coxeter functors
7 other sections not shown
abelian category admissible sequence assume bimodule commutative composition factors composition series connected valued graph continuous dimension type corresponding course Coxeter functors Coxeter transformation define denotes diagram dim Cr dimR direct sum direct summand division ring Dynkin graph easy endomorphism ring epimorphism equation equivalent Euclidian graph exact sequence Ext1 full exact embedding full subcategory Furthermore hence hereditary homomorphism i e r i,j e implies indecomposable modules induces injective ip(V isomorphic k e r K-algebra K-realization Lemma Let r,d linear M,ft matrices maximal morphism orbits pair polynomial positive roots preinjective preprojective projective Proof Proposition prove quadratic form R-linear regular representations representation type resp respect similar simple R-module simple regular sink skew fields submodule subobjects sum of copies tensor algebra Theorem uniserial vector spaces zero