2 citations · 5 across the 7 of their papers we have counts for
7 papers
The Gabriel-Roiter measures and representation type
Bo Chen
Let be an Artin algebra. A GR segment of is a sequence of GR measures which is closed under direct successors and direct predecessors. The number of the GR segments was con…
The GR-segments for tame quivers
Bo Chen
A GR-segment for an artin algebra is a sequence of Gabriel-Roiter measures, which is closed under direct predecessors and successors. The number of the GR-segments indexed by natur…
Regular modules with preprojective Gabriel-Roiter submodules over -Kronecker quivers
Bo Chen
Let be a wild -Kronecker quiver, i.e., a quiver with two vertices, labeled by 1 and 2, and arrows from 2 to 1. The indecomposable regular modules with preprojectiv…
The Gabriel-Roiter measures admitting no direct predecessors over -Kronecker quivers
Bo Chen
Let be an -Kronecker quiver, i.e., a quiver with two vertices, labeled by 1 and 2, and arrows from 2 to 1. We show that there are infinitely many Gabriel-Roiter measures…
The Gabriel-Roiter measures of the indecomposables in a regular component of the 3-Kronecker quiver
Bo Chen
Let be the 3-Kronecker quiver, i.e., has two vertices, labeled by 1 and 2, and three arrows from 2 to 1. Fix an algebraically closed field . Let be a regul…
The number of the Gabriel-Roiter measures admitting no direct predecessors over a wild quiver
Bo Chen
A famous result by Drozd says that a finite-dimensional representation-infinite algebra is of either tame or wild representation type. But one has to make assumption on the ground…
The Gabriel-Roiter measure for II
Bo Chen
Let be a tame quiver of type and $\Rep(Q)$ the category of finite dimensional representations over an algebraically closed field. A representation is…