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"Quiver" is the word used for "directed graph" in some parts of representation theory. The main reason to use the term quiver is to indicate an interest in considering representations of the quiver.

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"embedding" various matrix equivalences into the equivalence of particular linear map

Consider the square matrices over a (local) ring $R$, up to conjugation, $A\rightarrow UAU^{-1}$, where $U$ is an invertible matrix over $R$. Such an equivalence embeds into the "left-right" equivalen …