Triangulations of Prisms and Preprojective Algebras of Type <i>A</i>

Iyama, Osamu and Williams, Nicholas J (2024) Triangulations of Prisms and Preprojective Algebras of Type <i>A</i>. International Mathematics Research Notices: rnae059. ISSN 1073-7928

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Abstract

We show that isomorphism classes of indecomposable $\tau $-rigid pairs over $\Pi _{n}$, the preprojective algebra of $A_{n}$, are in bijection with internal $n$-simplices in the prism $\Delta _{n} \times \Delta _{1}$, the product of an $n$-simplex with a 1-simplex. We show further that this induces a bijection between triangulations of $\Delta _{n} \times \Delta _{1}$ and basic support $\tau $-tilting pairs over $\Pi _{n}$ such that bistellar flips of triangulations correspond to mutations of support $\tau $-tilting pairs. These bijections are shown to be compatible with the known bijections involving the symmetric group.

Item Type:
Journal Article
Journal or Publication Title:
International Mathematics Research Notices
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2600
Subjects:
?? general mathematicsmathematics(all) ??
ID Code:
218989
Deposited By:
Deposited On:
29 Apr 2024 14:10
Refereed?:
Yes
Published?:
Published
Last Modified:
28 Jul 2024 23:48