The incidence algebras of posets and acyclic categories

David Quinn

Research output: Contribution to journalArticle

Abstract

Acyclic categories were introduced by Kozlov and can be viewed as generalized 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 Gröbner basis with a lexicographic monomial order if and only if the poset or acyclic category is lexshellable.
Original languageEnglish
Pages (from-to)117-127
Number of pages11
JournalKyushu Journal of Mathematics
Volume67
Issue number1
DOIs
Publication statusPublished - Mar 2013

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Incidence Algebra
Poset
Path Algebra
Monomial
Quotient
If and only if

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The incidence algebras of posets and acyclic categories. / Quinn, David.

In: Kyushu Journal of Mathematics, Vol. 67, No. 1, 03.2013, p. 117-127.

Research output: Contribution to journalArticle

Quinn, David. / The incidence algebras of posets and acyclic categories. In: Kyushu Journal of Mathematics. 2013 ; Vol. 67, No. 1. pp. 117-127.
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