Editing Quiver (mathematics) (section)

== Quiver with relations ==
To enforce commutativity of some squares inside a quiver a generalization is the notion of quivers with relations (also named bound quivers).
A relation on a quiver {{mvar|Q}} is a {{mvar|K}} linear combination of paths from {{mvar|Q}}.
A quiver with relation is a pair {{math|(''Q'', ''I'')}} with {{mvar|Q}} a quiver and <math>I \subseteq K\Gamma</math> an
ideal of the path algebra. The quotient {{math|''K''&thinsp;Γ / ''I''}} is the path algebra of {{math|(''Q'', ''I'')}}.

===Quiver Variety===

Given the dimensions of the vector spaces assigned to every vertex, one can form a variety which characterizes all representations of that quiver with those specified dimensions, and consider stability conditions. These give quiver varieties, as constructed by {{harvtxt|King|1994}}.