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arXiv · 1501.02481

The incidence algebras of posets and acyclic categories

David Quinn
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Abstract

Acyclic categories were introduced by Kozlov and can be viewed as generalised posets. Similar to posets, one can define their incidence algebras and a related topological complex. We consider the incidence algebra of either a poset or acyclic category as the quotient of a path algebra by the parallel ideal. We show that this ideal has a quadratic Groeobner basis with a lexicographic monomial order if and only if the poset or acyclic category is lex-shellable.

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David Quinn. 2015-01-11. The incidence algebras of posets and acyclic categories. https://doi.org/10.2206/kyushujm.67.11767-1

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