Alexander Zimmermann
Comments on gentleness of endomorphism algebras.

Abstract.
In an earlier paper with Jan Schr\"oer we showed that for a special
biserial algebra $A$ the stable endomorphism algebra of a module $M$
with $Ext^1_A(M,M)=0$ is a so-called gentle algebra.
In this paper we compute as example the gentle algebras which occur as stable
endomorphism algebras of modules $M$ without self-extensions
over the Klein four group in characteristic $2$. Moreover, sharpening a
result in the earlier paper with Jan Schr\"oer, we show that if the
bounded derived category of an algebra $B$ can be embedded as
triangulated category into the derived category of a gentle algebra,
then $B$ is a gentle algebra as well.