44 research outputs found
Preprojective algebras and c-sortable words
Let be an acyclic quiver and be the complete preprojective
algebra of over an algebraically closed field . To any element in
the Coxeter group of , Buan, Iyama, Reiten and Scott have introduced and
studied in \cite{Bua2} a finite dimensional algebra . In
this paper we look at filtrations of associated to any reduced
expression of . We are especially interested in the case where
the word is -sortable, where is a Coxeter element. In this
situation, the consecutive quotients of this filtration can be related to
tilting -modules with finite torsionfree class.Comment: There was a mistake in section 4 of the previous version. This
section is removed in this new version. Some results still true of section 4
are now in subsection 3.3. Accepted for publication in Proc. of the London
Math. So
Lattice structure of torsion classes for path algebras
We consider module categories of path algebras of connected acyclic quivers.
It is shown in this paper that the set of functorially finite torsion classes
form a lattice if and only if the quiver is either Dynkin quiver of type A, D,
E, or the quiver has exactly two vertices.Comment: 10 pages. Minor errors are corrected, and references are updated in
the second versio