3 papers
math.RT2024
Gabriel's Theorem for Locally Finite-Dimensional Representations of Infinite Quivers
Nathaniel Gallup, Stephen Sawin
We prove a version of Gabriel's theorem for locally finite-dimensional representations of infinite quivers. Specifically, we show that if is any connected quiver, the category…
math.RT2023
Gabriel's Theorem for Infinite Quivers
Nathaniel Gallup, Stephen Sawin
We prove a version of Gabriel's theorem for (possibly infinite dimensional) representations of infinite quivers. More precisely, we show that the representation theory of quiver $Ω…
math.RT2022
Decompositions of Infinite-Dimensional Quiver Representations
Nathaniel Gallup, Stephen Sawin
Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph is Krull-Schmidt, as long as…