Morphisms and extensions between bricks over preprojective algebras of type A

Hanson, Eric J.; You, Xinrui

doi:10.1016/j.jalgebra.2023.10.019

Journal of Algebra

2024

DOI: 10.1016/j.jalgebra.2023.10.019

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Morphisms and extensions between bricks over preprojective algebras of type A

Eric J. Hanson,

Xinrui You

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2024

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Triangulations of Prisms and Preprojective Algebras of Type A

Iyama,

Williams

2024

International Mathematics Research Notices

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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.

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Triangulations of Prisms and Preprojective Algebras of Type A

Iyama,

Williams

2024

International Mathematics Research Notices

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show abstract

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Morphisms and extensions between bricks over preprojective algebras of type A

Cited by 1 publication

References 30 publications

Triangulations of Prisms and Preprojective Algebras of Type A

Triangulations of Prisms and Preprojective Algebras of Type A

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