Rigid quivers and rigid algebras

TY - JOUR

T1 - Rigid quivers and rigid algebras

AU - Cagliero, Leandro

AU - Tirao, Paulo

PY - 2008/10/1

Y1 - 2008/10/1

N2 - We define a quiver to be rigid if all the associated truncated quiver algebras are rigid. The rigidity of quivers is then determined by the combinatorics of the set of pairs of parallel paths of the underlying quiver as follows from Cibils' criteria for the rigidity of truncated quiver algebras. In this paper we characterize rigid quivers Δ and relate this characterization with the condensed quiver and the quiver of beads of Δ, two much simpler quivers associated to Δ. The first one is a well-known object and the second one is introduced by us to this end.

AB - We define a quiver to be rigid if all the associated truncated quiver algebras are rigid. The rigidity of quivers is then determined by the combinatorics of the set of pairs of parallel paths of the underlying quiver as follows from Cibils' criteria for the rigidity of truncated quiver algebras. In this paper we characterize rigid quivers Δ and relate this characterization with the condensed quiver and the quiver of beads of Δ, two much simpler quivers associated to Δ. The first one is a well-known object and the second one is introduced by us to this end.

KW - Combinatorics of quivers

KW - Deformations of algebras

KW - Hochschild cohomology of truncated quiver algebras

UR - http://www.scopus.com/inward/record.url?scp=49549118421&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2008.05.034

DO - 10.1016/j.jalgebra.2008.05.034

M3 - 文章

AN - SCOPUS:49549118421

VL - 320

SP - 2827

EP - 2846

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 7

ER -