12 citations · 28 across the 16 of their papers we have counts for
6 papers · 1 filter
On 2-representation infinite algebras arising from dimer models
Yusuke Nakajima
The Jacobian algebra arising from a consistent dimer model is a bimodule -Calabi-Yau algebra, and its center is a -dimensional Gorenstein toric singularity. A perfect matchin…
Non-commutative crepant resolutions of Hibi rings with small class group
Yusuke Nakajima
In this paper, we study splitting (or toric) non-commutative crepant resolutions (= NCCRs) of some toric rings. In particular, we consider Hibi rings, which are toric rings arising…
Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
Akihiro Higashitani, Yusuke Nakajima
In this paper, we study divisorial ideals of a Hibi ring which is a toric ring arising from a partially ordered set. We especially characterize the special class of divisorial idea…
Semi-steady non-commutative crepant resolutions via regular dimer models
Yusuke Nakajima
A consistent dimer model gives a non-commutative crepant resolution (= NCCR) of a -dimensional Gorenstein toric singularity. In particular, it is known that a consistent dimer m…
Mutations of splitting maximal modifying modules: The case of reflexive polygons
Yusuke Nakajima
It is known that every three dimensional Gorenstein toric singularity has a crepant resolution. Although it is not unique, all crepant resolutions are connected by repeating the op…
On steady non-commutative crepant resolutions
Osamu Iyama, Yusuke Nakajima
We introduce special classes of non-commutative crepant resolutions (= NCCR) which we call steady and splitting. We show that a singularity has a steady splitting NCCR if and only…