Noncommutative crepant resolutions of Hibi rings with small class group
Abstract
In this paper, we study splitting (or toric) noncommutative crepant resolutions (= NCCRs) of some toric rings. In particular, we consider Hibi rings, which are toric rings arising from partially ordered sets, and show that Gorenstein Hibi rings with class group $\mathbb{Z}^2$ have a splitting NCCR. In the appendix, we also discuss Gorenstein toric rings with class group $\mathbb{Z}$, in which case the existence of splitting NCCRs is already known. We especially observe the mutations of modules giving splitting NCCRs for the three dimensional case, and show the connectedness of the exchange graph.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1801.05139
 arXiv:
 arXiv:1801.05139
 Bibcode:
 2018arXiv180105139N
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry
 EPrint:
 20 pages, to appear in J. Pure Appl. Algebra, v2: major changes, in particular the structure of Section3 was changed for improving readability