Incidence algebras and coalgebras of decomposition structures
type: Item
instance of: scholarly article
title: Incidence algebras and coalgebras of decomposition structures
zbMATH Open document ID: 0698.05005
DOI: 10.1016/0012-365X(90)90028-G
author: Luigi Azzena
author: Fracesco Piras
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The notion of incidence algebra was introduced by G.-C. Rota and others in order to supply a unified algebraic setting for a wide class of problems known from enumerative combinatorics. The procedure used was originally associated with locally finite posets and monoids with the finite factorization property, but then it was extended to the set of morphisms of a decomposition-finite category. The study of so-called incidence coalgebras has proved useful. In the present paper, the authors study the reciprocal relations between the set \({\mathcal S}\) of morphisms of a given category, its incidence algebra A(\({\mathcal S})\) and the incidence coalgebra C(\({\mathcal S})\). The main propositions generalize results relating to categories and posets. The authors prove that all automorphisms and derivations of an incidence algebra of a finitely generated decomposition structure are continuous with respect to finite topology.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 4143980
zbMATH Keywords: Möbius inversion
zbMATH Keywords: decomposition-finite category
zbMATH Keywords: incidence algebra
zbMATH Keywords: incidence coalgebra
reviewed by: Jiri Vinarek
MaRDI profile type: Publication
cites work: Automorphisms and derivations of incidence algebras
cites work: Model theory
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cites work: Coalgebras and Bialgebras in Combinatorics
cites work: Une théorie combinatoire des séries formelles
cites work: The isomorphism problem for incidence algebras of Möbius categories
cites work: Structure of incidence algebras and their automorphism groups
cites work: Q5590089
full work available at URL: 0012-365x(90)90028-g
OpenAlex ID: W2084800416
description: scientific article; zbMATH DE number 4143980