Junyang Liu

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math.RT2026

Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets

Osamu Iyama, Junyang Liu

We prove that for any $N$ -graded Gorenstein tiled order $A$ , the stable category $CM^{Z} A$ is triangle equivalent to the perfect derived cate…

math.RT2026

Calabi-Yau structures on derived and singularity categories of symmetric orders

Norihiro Hanihara, Junyang Liu

We construct left and right Calabi-Yau structures on derived respectively singularity categories of symmetric orders $I^$ over commutative Gorenstein rings $R$ . For this, we first…

math.RT2025

Tilting theory for hypersurface singularities of dimension one

Osamu Iyama, Junyang Liu

Any $N$ -graded commutative Gorenstein ring $R$ of Krull dimension one with $R_{0}$ a field admits a standard silting object $V$ in the stable category $\underline{\mathrm{CM…

math.RT2025

$A_{\infty}$ -deformations of zigzag algebras via Ginzburg dg algebras

Junyang Liu, Zhengfang Wang

This note aims to give a short proof of the recent result due to EtgÃ¼-Lekili (2017) and Lekili-Ueda (2021): the zigzag algebra of any finite tree over a field of characteristic 0…

Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets

Calabi-Yau structures on derived and singularity categories of symmetric orders

Tilting theory for hypersurface singularities of dimension one

A∞​-deformations of zigzag algebras via Ginzburg dg algebras

$A_{\infty}$ -deformations of zigzag algebras via Ginzburg dg algebras