In mathematics a quiver is the same thing Essentially, a quiver is a directed graph with no limitations. The case of finite Dynkin diagrams and Gabriels theorem. Description of simple, projective and injective modules. In what follows we shall consider only finite quivers. Quivers In colloquial English, Definition (Quiver) noun: quiver plural noun: quivers an archer’s portable case for holding arrows. Representations of quivers - equivalence with modules over the path algebra. For an arrow aEwe refer to the point s(a) V as the start vertex of aand to the point t(a) as the target vertex of a. In mathematics a quiver is the same thing Essentially, a quiver is a directed graph with no limitations. Definition 2.1A finitequiver is a quadruple Q (V,E,s,t) where V is a finite set of vertices, Eis a finite set ofarrows, and s,t: EV are two maps. Meaning: An arrow in the quiver is a strategy or option that could be used to achieve your objective. Kirillov, Quiver representations and quiver varieties. In colloquial English, Definition (Quiver) noun: quiver plural noun: quivers an archer’s portable case for holding arrows. This fits nicely with Gabriel's theorem: the dimensions of these representations are $(1,0)$, $(1,1)$ and $(0,1)$, which correspond to the three positive roots of the algebra $A_2$. $$0 : k \rightarrow 0 \, \qquad 1 : k \rightarrow k \,, \qquad 0 : 0 \rightarrow k \. We have found three indecomposable representations, Clearly it is not semisimple, but it is indecomposable. The representation $1 : k \rightarrow k$ is not simple (because it is not of the type $S(i)$), indeed it contains $0 : k \rightarrow 0$ as a subrepresentation.These are the representations that we called $S(1)$ and $S(2)$ above. A quiver is a holder used to store and transport arrows. The representation $0 : k \rightarrow k$ is actually semisimple, it can be decomposed as the sum of the two simple representations $0 : k \rightarrow 0$ and $0 : 0 \rightarrow k$.This means that any representation is (isomorphic to) a direct sum of representations of the type $1 : k \rightarrow k$ and $0 : k \rightarrow k$. A quiver $\vec$ is the unit $r \times r$ matrix.
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