Some Computations for Binomial Edge Ideals and Koszul Duality
Abstract
We make some observations on binomial edge ideals, with the characterization of their Koszulness as motivation. Inspired by results of Ene, Herzog and Hibi, we discuss building Koszul graphs from smaller pieces in a controlled manner. We characterize the Koszul property of cone graphs and compute the dual algebra of the quadratic algebra coming from an arbitrary binomial edge ideal. We compute the first two syzygies of the infinite minimal free resolution of the residue field over the algebra defined by a binomial edge ideal, and observe that they are always linear.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.3542
 Bibcode:
 2014arXiv1412.3542K
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics
 EPrint:
 5 pages