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Stability, shards, and preprojective algebras (1706.00164v1)
Published 1 Jun 2017 in math.RT and math.CO
Abstract: The goal of this note two-fold. First, I draw attention to the way that semistability (in the sense of King) gives us a geometrical picture of (some of) the extension-closed abelian subcategories of a finite-dimensional algebra. Second, I describe Nathan Reading's shards of a hyperplane arrangement, and explain their relevance to understanding the semistability picture for finite-type preprojective algebras.