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To this direction, we\ngive basic category-theoretic definitions and prove basic properties of alge-\nbras, coalgebras and Hopf algebras as well as the structures of tensor algebra\nand universal enveloping algebra of a Lie algebra. Using dilations and the\nspectral decomposition they induce in a bialgebra we prove the two central\nstructure theorems of Hopf algebras." }, { "@language" : "el", "@value" : "Σκοπός της παρούσας διπλωματικής εργασίας η οποία είναι βασισμένη στο\nσύγγραμα Classical Hopf Algebras and their Applications των Pierre Cartier\nκαι Frédéric Patras είναι η διατύπωση και παρουσίαση των θεωρημάτων δομής\nPoincaré - Birkhoff - Witt και Cartier των Hopf αλγεβρών. Στην κατεύθυνση\nαυτή διατυπώνονται οι κατηγοριοθεωρητικοί ορισμοί και αποδεικνύονται ιδιότητες\nτων αλγεβρών, των co-αλγεβρών, των Hopf αλγεβρών καθώς και δομών όπως η\nτανυστική άλγεβρα και η καθολική enveloping άλγεβρα μιας Lie άλγεβρας. Με\nτην χρήση των διαστολών (dilations) και της φασματικής ανάλυσης που αυτές\nεπάγουν σε μια bi-άλγεβρα αποδεικνύονται δύο σημαντικά θεωρήματα δομής\nτης θεωρίας των Hopf αλγεβρών." } ], "identifier" : "uoadl:3401210", "language" : "eng", "dc:rights" : { "@id" : "https://creativecommons.org/licenses/by-nc/4.0/" }, "subject" : [ { "@language" : "el", "@value" : "Θετικές Επιστήμες" }, { "@id" : "http://semantics.gr/authorities/EKT-voc-classifier/375615523" }, { "@language" : "en", "@value" : "Science" } ], "title" : "The Poincaré - Birkhoff - Witt and Cartier structure theorems of Hopf algebras", "type" : [ { "@language" : "el", "@value" : "Διπλωματική Εργασία" }, "born_digital_postgraduate_thesis", { "@id" : "http://semantics.gr/authorities/openarchives-item-types/metaptyxiakh-ergasia" }, { "@language" : "en", "@value" : "Postgraduate Thesis" } ], "created" : "2024" } ], "@context" : { "rights" : { "@id" : "http://www.europeana.eu/schemas/edm/rights", "@type" : "@id" }, "provider" : { "@id" : "http://www.europeana.eu/schemas/edm/provider" }, "object" : { "@id" : "http://www.europeana.eu/schemas/edm/object", "@type" : "@id" }, "isShownAt" : { "@id" : "http://www.europeana.eu/schemas/edm/isShownAt", "@type" : "@id" }, "dataProvider" : { "@id" : "http://www.europeana.eu/schemas/edm/dataProvider" }, "aggregatedCHO" : { "@id" : "http://www.europeana.eu/schemas/edm/aggregatedCHO", "@type" : "@id" }, "exactMatch" : { "@id" : "http://www.w3.org/2004/02/skos/core#exactMatch", "@type" : "@id" }, "narrowMatch" : { "@id" : "http://www.w3.org/2004/02/skos/core#narrowMatch", "@type" : "@id" }, "narrower" : { "@id" : "http://www.w3.org/2004/02/skos/core#narrower", "@type" : "@id" }, "prefLabel" : { "@id" : "http://www.w3.org/2004/02/skos/core#prefLabel" }, "note" : { "@id" : "http://www.w3.org/2004/02/skos/core#note" }, "closeMatch" : { "@id" : "http://www.w3.org/2004/02/skos/core#closeMatch", "@type" : "@id" }, "broader" : { "@id" : "http://www.w3.org/2004/02/skos/core#broader", "@type" : "@id" }, "title" : { "@id" : "http://purl.org/dc/elements/1.1/title" }, "subject" : { "@id" : "http://purl.org/dc/elements/1.1/subject" }, "type" : { "@id" : "http://purl.org/dc/elements/1.1/type" }, "creator" : { "@id" : "http://purl.org/dc/elements/1.1/creator" }, "description" : { "@id" : "http://purl.org/dc/elements/1.1/description" }, "identifier" : { "@id" : "http://purl.org/dc/elements/1.1/identifier" }, "created" : { "@id" : "http://purl.org/dc/terms/created" }, "language" : { "@id" : "http://purl.org/dc/elements/1.1/language" }, "ore" : "http://www.openarchives.org/ore/terms/", "owl" : "http://www.w3.org/2002/07/owl#", "svcs" : "http://rdfs.org/sioc/services#", "skos" : "http://www.w3.org/2004/02/skos/core#", "rdfs" : "http://www.w3.org/2000/01/rdf-schema#", "rdaGr2" : "http://rdvocab.info/ElementsGr2/", "edm" : "http://www.europeana.eu/schemas/edm/", "ekt" : "https://www.semantics.gr/authorities/schemanamespaces/ekt#", "doap" : "http://usefulinc.com/ns/doap#", "rdf" : "http://www.w3.org/1999/02/22-rdf-syntax-ns#", "xalan" : "http://xml.apache.org/xalan", "dcterms" : "http://purl.org/dc/terms/", "wgs84_pos" : "http://www.w3.org/2003/01/geo/wgs84_pos#", "foaf" : "http://xmlns.com/foaf/0.1/", "crm" : "http://www.cidoc-crm.org/rdfs/cidoc_crm_v5.0.2_english_label.rdfs#", "dc" : "http://purl.org/dc/elements/1.1/" } }