## On Algebras of Finite Representation Type |

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abelian category assume basis of F bimodule complement Consequently consider decompose decomposition is compatible denote diagram dim F dim U_ dimension functor direct decomposition direct sum Dynkin diagrams elements epimorphism equivalent exact subcategory F-basis field F finite dimensional K-algebra finite number finite type follows full embedding full subcategory G c F G X G G-subspace given Grothendieck category Hence HomG Horn idempotent inclusion indecomposable representations indecomposable S-spaces index set induction isomorphic K-species of finite K-species Q K-structure ker cp Kl Kl Lemma modular law monomorphism Moreover morphism number of indecomposable obviously projective proof of Theorem Proposition 5.2 representation of Q Rm(Q simple objects strongly unbounded type subcategory of S(S subfield of F subobject sum of copies u2 n v uL n u2 vector space whereas