Incidence algebras of simplicial complexes

Roman R. Zapatrin

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arXiv · math/0001065

Incidence algebras of simplicial complexes

Roman R. Zapatrin

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Abstract

With any locally finite partially ordered set $K$ its incidence algebra $Ω(K)$ is associated. We shall consider algebras over fields with characteristic zero. In this case there is a correspondence $K \leftrightarrow Ω(K)$ 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 $K\leftrightarrowΩ(K)$ is a contravariant functor.

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Roman R. Zapatrin. 2000-01-12. Incidence algebras of simplicial complexes. https://arxiv.org/abs/math/0001065

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