Incidence algebras of simplicial complexes

Details Incidence algebras of simplicial complexes Incidence algebras of simplicial complexes

2000-01-12

arxiv.org/abs/math/0001065v1

Pure Mathematics and Applications, 11, 105-118 (2001)

Mathematics

Combinatorics

LaTex2e, 14 pages

Scientific paper

With any locally finite partially ordered set $K$ its incidence algebra $\Omega(K)$ is associated. We shall consider algebras over fields with characteristic zero. In this case there is a correspondence $K \leftrightarrow \Omega(K)$ such that the poset $K$ can be reconstructed from its incidence algebra up to an isomorphism -- due to Stanley theorem. In the meantime, a monotone mapping between two posets in general induces no homomorphism of their incidence algebras. In this paper I show that if the class of posets is confined to simplicial complexes then their incidence algebras acquire the structure of differential moduli and the correspondence $K\leftrightarrow\Omega(K)$ is a contravariant functor.

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