On isomorphism of simplicial complexes and their related algebras
Commutative Algebra
2010-10-12 v1 Combinatorics
Abstract
In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as -algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as -algebras. Based on an explicit -algebra isomorphism of two Stanley-Reisner rings, or facet rings or edge rings, we present a fast algorithm to find explicitly the isomorphism of the associated simplicial complexes, or graphs.
Cite
@article{arxiv.math/0702618,
title = {On isomorphism of simplicial complexes and their related algebras},
author = {Rashid Zaare-Nahandi},
journal= {arXiv preprint arXiv:math/0702618},
year = {2010}
}