On isomorphism of simplicial complexes and their related algebras

Details On isomorphism of simplicial complexes and their related algebras On isomorphism of simplicial complexes and their related algebras

2007-02-21

arxiv.org/abs/math/0702618v1

Bulletin of the Iranian Math. Soc., 38 (2009) no. 2, 41--48

Mathematics

Commutative Algebra

Scientific paper

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 $K$-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as $K$-algebras. Based on an explicit $K$-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.

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