The strong no loop conjecture is true for mild algebras

Details The strong no loop conjecture is true for mild algebras The strong no loop conjecture is true for mild algebras

2010-11-04

arxiv.org/abs/1011.1143v2

Mathematics

Representation Theory

Scientific paper

Let A be a finite dimensional associative algebra over an algebraically closed field with a simple module S of finite projective dimension. The strong no loop conjecture says that this implies Ext(S,S)=0, i.e. that the quiver of A has no loops in the point corresponding to S. In this paper we prove the conjecture in case A is mild, which means that A has only finitely many two-sided ideals and each proper factor algebra A/J is representation finite. In fact, it is sufficient that a "small neighborhood" of the support of the projective cover of S is mild.

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