The finiteness conjecture for direct sums of quivers

Let QQ and QQ' be quivers such that Ψ(Q)\Psi(Q) and Ψ(Q)\Psi(Q') are finite and non-empty, and let QQQ\oplus Q' denote their direct sum. Direct-sum finiteness conjecture. Then Ψ(QQ)\Psi(Q\oplus Q') is finite and non-empty. This proposed relationship concerns the behavior of the graph Ψ\Psi under direct sums of quivers. It is presented as an open conjectural direction following a theorem about maximal green sequences for direct sums.

Sources & referencesView supporting material

Primary source

John W. Lawson and Matthew R. Mills, “Properties of minimal mutation-infinite quivers”, arXiv:1610.08333 (2016).

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