On some homological conjectures for finite dimensional algebras
Skorodumov
Denis
Skorodumov, Denis
aut
2011-02-17
2014-08-12
en
Let A be a mild k-algebra over an algebraically closed field k, i.e. A is representation-finite or distributive of minimal representation-infinite type. Let S be a simple A-module of finite projective dimension. We establish the strong no loop conjecture for A, which claims that S has only split self-extensions, i.e. the quiver of A has no loop at the vertex corresponding to S. More generally we show that only a small neighborhood of the support of the projective cover of S has to be mild.<br>
Furthermore some reduction techniques are developed for the stronger no loop conjecture and the finitistic dimension conjecture.
urn:nbn:de:hbz:468-20110225-103745-4
2014-08-12T08:32:51.291Z
2014-08-12T09:18:19.086Z
published
Diss
fbc/mathematik/diss2011/skorodumov