The incidence algebras of posets and acyclic categories
Rings and Algebras
2015-01-13 v1
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.
Keywords
Cite
@article{arxiv.1501.02481,
title = {The incidence algebras of posets and acyclic categories},
author = {David Quinn},
journal= {arXiv preprint arXiv:1501.02481},
year = {2015}
}
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11 pages