Duality for quasipolytopes

Anna Mućka , Anna Romanowska

Abstract

In an earlier paper, Romanowska, Ślusarski and Smith described a duality between the category of polytopes (finitely generated real convex sets considered as barycentric algebras) and a certain category of intersections of hypercubes, considered as barycentric algebras with additional constant operations. The present paper provides an extension of this duality to a much more general class of so-called quasipolytopes, that is, convex sets with polytopes as closures. The dual spaces of quasipolytopes are Płonka sums of open polytopes, which are considered as barycentric algebras with some additional operations. In constructing this duality, we use several known and new dualities: the Hofmann–Mislove–Stralka duality for semilattices; the Romanowska–Ślusarski–Smith duality for polytopes; a new duality for open polytopes; and a new duality for injective Płonka sums of polytopes.
Author Anna Mućka ZRRC
Anna Mućka,,
- Department of Partial Differential Equations
, Anna Romanowska ZAK
Anna Romanowska,,
- Department of Algebra and Combinatorics
Journal seriesJournal of the Australian Mathematical Society, ISSN 1446-7887
Issue year2016
Vol101
No1
Pages95-117
Publication size in sheets1.1
Keywords in Englishmode, affine space, convex set, baricentrix algebra,variety regulation, Płonka sum, duality
Abstract in PolishQuasi-wielościanami (quasipolytopes) nazywamy zbiory wypukłe, których domknięcie jest wielościanem. Traktowane są one w przedstawionej pracy jako algebry barycentryczne. Głównym wynikiem jest opisanie dualności kategoryjnej między klasą takich wielościanów a pewną klasą algebr barycentrycznych z dodatkowymi operacjami. Wynik ten w istotny sposób uogólnia wcześniejszy wynik Romanowskiej, Smitha i Ślusarskiego opisujący dualność dla wielościanów.
DOIDOI:10.1017/S1446788715000683
URL http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10392150
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 15.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.656 (2) - 2016=0.537 (5)
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