The incidence algebras of posets and acyclic categories
arXiv:1501.02481 · doi:10.2206/kyushujm.67.11767-1
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.
11 pages