{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7RIUPI6F/139081af-4ce1-48d4-b8f9-91c2cd62fc4b/PDF","dcterms:extent":"327 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7RIUPI6F/a16013c3-5df4-46e5-afc2-e6cee77dc01f/TEXT","dcterms:extent":"30 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-7RIUPI6F","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":"Sumalroj, Supalak","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 185-202"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18953817","URN:URN:NBN:SI:doc-7RIUPI6F"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"distance-regular graph"},{"@xml:lang":"sl","#text":"podkonstitutivna algebra"},{"@xml:lang":"sl","#text":"razdaljno-regularen graf"},{"@xml:lang":"en","#text":"subconstituent algebra"},{"@xml:lang":"en","#text":"Terwilliger algebra"},{"@xml:lang":"sl","#text":"Terwilligerjeva algebra"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A diagram associated with the subconstituent algebra of a distance-regular graph|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper we consider a distance-regular graph ?$\\Gamma$?. Fix a vertex ?$x$? of ?$\\Gamma$? and consider the corresponding subconstituent algebra ?$T = T(x)$?. The algebra ?$T$? is the ?$\\mathbb{C}$?-algebra generated by the Bose-Mesner algebra ?$M$? of ?$\\Gamma$? and the dual Bose-Mesner algebra ?$M^\\ast$? of ?$\\Gamma$? with respect to ?$x$?. We consider the subspaces ?$M, M^\\ast, MM^\\ast, M^\\ast M, MM^\\ast M, M^\\ast MM^\\ast, \\dots$? along with their intersections and sums. In our notation, ?$MM^\\ast$? means Span?$\\{RS \\mid R \\in M, S \\in M^\\ast\\}$?, and so on. We introduce a diagram that describes how these subspaces are related. We describe in detail that part of the diagram up to ?$MM^\\ast + M^\\ast M$?. For each subspace ?$U$? shown in this part of the diagram, we display an orthogonal basis for ?$U$? along with the dimension of ?$U$?. For an edge ?$U \\subseteq W$? from this part of the diagram, we display an orthogonal basis for the orthogonal complement of ?$U$? in ?$W$? along with the dimension of this orthogonal complement"},{"@xml:lang":"sl","#text":"V tem članku obravnavamo razdaljno-regularen graf ?$\\Gamma$?. Fiksiramo vozlišce ?$x$? grafa ?$\\Gamma$? in obravnavamo prirejeno Terwilligerjevo algebro ?$T = T(x)$?. Algebra ?$T$? je ?$\\mathbb{C}$?-algebra, generirana z Bose-Mesnerjevo algebro ?$M$? grafa ?$\\Gamma$? in dualno Bose-Mesnerjevo algebro ?$M^\\ast$? grafa ?$\\Gamma$? glede na ?$x$?. Obravnavamo podprostore ?$M, M^\\ast, MM^\\ast, M^\\ast M, MM^\\ast M, M^\\ast MM^\\ast, \\dots$? ter njihove preseke in vsote. Pri tem ?$MM^\\ast$? pomeni Span?$\\{RS \\mid R \\in M, S \\in M^\\ast\\}$? in tako dalje. Uvedemo diagram, ki opisuje, kako so ti podprostori povezani med seboj. Podrobno opišemo del tega diagrama vse do ?$MM^\\ast + M^\\ast M$?. Za vsak podprostor ?$U$?, prikazan v tem delu diagrama, podamo njegovo ortogonalno bazo ter njegovo dimenzijo. Za povezavo ?$U \\subseteq W$? iz tega dela diagrama podamo ortogonalno bazo ortogonalnega komplementa podprostora ?$U$? v prostoru ?$W$? ter dimenzijo tega ortogonalnega komplementa"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-7RIUPI6F","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7RIUPI6F"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7RIUPI6F/139081af-4ce1-48d4-b8f9-91c2cd62fc4b/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-7RIUPI6F/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7RIUPI6F"}}}}