Matches in SemOpenAlex for { <https://semopenalex.org/work/W1567894031> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W1567894031 endingPage "1509" @default.
- W1567894031 startingPage "1487" @default.
- W1567894031 abstract "We build upon Mac Lane’s definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the existing notions of product systems fit into our categorical framework, as do the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-graphs of Kumjian and Pask. We then specialize to product systems over right-angled Artin semigroups; these are semigroups that interpolate between free semigroups and free abelian semigroups. For such a semigroup we characterize all product systems which take values in a given tensor groupoid <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In particular, we obtain necessary and sufficient conditions under which a collection of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding=application/x-tex>1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-graphs form the coordinate graphs of a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-graph." @default.
- W1567894031 created "2016-06-24" @default.
- W1567894031 creator A5050112257 @default.
- W1567894031 creator A5091380066 @default.
- W1567894031 date "2001-11-30" @default.
- W1567894031 modified "2023-10-03" @default.
- W1567894031 title "Product systems over right-angled Artin semigroups" @default.
- W1567894031 cites W1974069850 @default.
- W1567894031 cites W1977621603 @default.
- W1567894031 cites W1998010282 @default.
- W1567894031 cites W2086158278 @default.
- W1567894031 cites W2095538806 @default.
- W1567894031 cites W2261782167 @default.
- W1567894031 cites W2592551138 @default.
- W1567894031 cites W2963153751 @default.
- W1567894031 doi "https://doi.org/10.1090/s0002-9947-01-02911-7" @default.
- W1567894031 hasPublicationYear "2001" @default.
- W1567894031 type Work @default.
- W1567894031 sameAs 1567894031 @default.
- W1567894031 citedByCount "58" @default.
- W1567894031 countsByYear W15678940312012 @default.
- W1567894031 countsByYear W15678940312013 @default.
- W1567894031 countsByYear W15678940312014 @default.
- W1567894031 countsByYear W15678940312015 @default.
- W1567894031 countsByYear W15678940312016 @default.
- W1567894031 countsByYear W15678940312017 @default.
- W1567894031 countsByYear W15678940312018 @default.
- W1567894031 countsByYear W15678940312019 @default.
- W1567894031 countsByYear W15678940312020 @default.
- W1567894031 countsByYear W15678940312021 @default.
- W1567894031 countsByYear W15678940312022 @default.
- W1567894031 crossrefType "journal-article" @default.
- W1567894031 hasAuthorship W1567894031A5050112257 @default.
- W1567894031 hasAuthorship W1567894031A5091380066 @default.
- W1567894031 hasBestOaLocation W15678940311 @default.
- W1567894031 hasConcept C11413529 @default.
- W1567894031 hasConcept C136119220 @default.
- W1567894031 hasConcept C154945302 @default.
- W1567894031 hasConcept C184337299 @default.
- W1567894031 hasConcept C18903297 @default.
- W1567894031 hasConcept C199360897 @default.
- W1567894031 hasConcept C202444582 @default.
- W1567894031 hasConcept C2524010 @default.
- W1567894031 hasConcept C2776321320 @default.
- W1567894031 hasConcept C2777212361 @default.
- W1567894031 hasConcept C2777299769 @default.
- W1567894031 hasConcept C33923547 @default.
- W1567894031 hasConcept C41008148 @default.
- W1567894031 hasConcept C51255310 @default.
- W1567894031 hasConcept C86803240 @default.
- W1567894031 hasConcept C90673727 @default.
- W1567894031 hasConceptScore W1567894031C11413529 @default.
- W1567894031 hasConceptScore W1567894031C136119220 @default.
- W1567894031 hasConceptScore W1567894031C154945302 @default.
- W1567894031 hasConceptScore W1567894031C184337299 @default.
- W1567894031 hasConceptScore W1567894031C18903297 @default.
- W1567894031 hasConceptScore W1567894031C199360897 @default.
- W1567894031 hasConceptScore W1567894031C202444582 @default.
- W1567894031 hasConceptScore W1567894031C2524010 @default.
- W1567894031 hasConceptScore W1567894031C2776321320 @default.
- W1567894031 hasConceptScore W1567894031C2777212361 @default.
- W1567894031 hasConceptScore W1567894031C2777299769 @default.
- W1567894031 hasConceptScore W1567894031C33923547 @default.
- W1567894031 hasConceptScore W1567894031C41008148 @default.
- W1567894031 hasConceptScore W1567894031C51255310 @default.
- W1567894031 hasConceptScore W1567894031C86803240 @default.
- W1567894031 hasConceptScore W1567894031C90673727 @default.
- W1567894031 hasIssue "4" @default.
- W1567894031 hasLocation W15678940311 @default.
- W1567894031 hasLocation W15678940312 @default.
- W1567894031 hasOpenAccess W1567894031 @default.
- W1567894031 hasPrimaryLocation W15678940311 @default.
- W1567894031 hasRelatedWork W1560139384 @default.
- W1567894031 hasRelatedWork W1996319902 @default.
- W1567894031 hasRelatedWork W2070511061 @default.
- W1567894031 hasRelatedWork W2101026640 @default.
- W1567894031 hasRelatedWork W2267636672 @default.
- W1567894031 hasRelatedWork W2783157960 @default.
- W1567894031 hasRelatedWork W2804929216 @default.
- W1567894031 hasRelatedWork W3202191715 @default.
- W1567894031 hasRelatedWork W3214915308 @default.
- W1567894031 hasRelatedWork W803934970 @default.
- W1567894031 hasVolume "354" @default.
- W1567894031 isParatext "false" @default.
- W1567894031 isRetracted "false" @default.
- W1567894031 magId "1567894031" @default.
- W1567894031 workType "article" @default.