Homological embeddings for preprojective algebras

الأصل · EN

For a fixed finite dimensional algebra A, we study representation embeddings of the form mod(B)→ mod(A). Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only Ext¹ is preserved. In case A is a preprojective algebra of Dynkin type, we give an explicit classification of all weakly homological and homological embeddings. Furthermore, we show that for self-injective algebras a classification of homological embeddings becomes accessible once these algebras fulfil the Tachikawa conjecture.