Publication Information

{'id': 'https://openalex.org/W2800291541', 'doi': None, 'title': 'Roots of asymmetric geometric representations of Coxeter groups', 'display_name': 'Roots of asymmetric geometric representations of Coxeter groups', 'publication_year': 2007, 'publication_date': '2007-07-23', 'ids': {'openalex': 'https://openalex.org/W2800291541', 'mag': '2800291541'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://arxiv.org/abs/0707.3310v2', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'posted-content', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5004498823', 'display_name': 'Robert G. Donnelly', 'orcid': 'https://orcid.org/0000-0001-8193-7943'}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Robert G. Donnelly', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5004498823'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.816, 'has_fulltext': False, 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.48855, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 76, 'max': 78}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9995, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.995, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/coxeter-graph', 'display_name': 'Coxeter graph', 'score': 0.5198398}, {'id': 'https://openalex.org/keywords/root', 'display_name': 'Root (linguistics)', 'score': 0.41708368}], 'concepts': [{'id': 'https://openalex.org/C143669375', 'wikidata': 'https://www.wikidata.org/wiki/Q7874246', 'display_name': 'Coxeter group', 'level': 2, 'score': 0.9854003}, {'id': 'https://openalex.org/C140860697', 'wikidata': 'https://www.wikidata.org/wiki/Q5179941', 'display_name': 'Coxeter element', 'level': 3, 'score': 0.88011783}, {'id': 'https://openalex.org/C48495023', 'wikidata': 'https://www.wikidata.org/wiki/Q6673739', 'display_name': 'Longest element of a Coxeter group', 'level': 5, 'score': 0.87432957}, {'id': 'https://openalex.org/C37486056', 'wikidata': 'https://www.wikidata.org/wiki/Q5179939', 'display_name': 'Coxeter complex', 'level': 4, 'score': 0.8214634}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.82003367}, {'id': 'https://openalex.org/C40233952', 'wikidata': 'https://www.wikidata.org/wiki/Q768074', 'display_name': 'Weyl group', 'level': 2, 'score': 0.74725986}, {'id': 'https://openalex.org/C201064014', 'wikidata': 'https://www.wikidata.org/wiki/Q3956993', 'display_name': 'Artin group', 'level': 3, 'score': 0.62761027}, {'id': 'https://openalex.org/C57796230', 'wikidata': 'https://www.wikidata.org/wiki/Q899720', 'display_name': 'Point group', 'level': 2, 'score': 0.6056758}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.54657084}, {'id': 'https://openalex.org/C27225450', 'wikidata': 'https://www.wikidata.org/wiki/Q3115477', 'display_name': 'Coxeter graph', 'level': 5, 'score': 0.5198398}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, 'score': 0.5033631}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.48483574}, {'id': 'https://openalex.org/C171078966', 'wikidata': 'https://www.wikidata.org/wiki/Q111029', 'display_name': 'Root (linguistics)', 'level': 2, 'score': 0.41708368}, {'id': 'https://openalex.org/C41895202', 'wikidata': 'https://www.wikidata.org/wiki/Q8162', 'display_name': 'Linguistics', 'level': 1, 'score': 0.079327345}, {'id': 'https://openalex.org/C22149727', 'wikidata': 'https://www.wikidata.org/wiki/Q7940747', 'display_name': 'Voltage graph', 'level': 4, 'score': 0.07328737}, {'id': 'https://openalex.org/C203776342', 'wikidata': 'https://www.wikidata.org/wiki/Q1378376', 'display_name': 'Line graph', 'level': 3, 'score': 0.066193074}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://arxiv.org/abs/0707.3310v2', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 10, 'referenced_works': ['https://openalex.org/W112671161', 'https://openalex.org/W1995010619', 'https://openalex.org/W2009190506', 'https://openalex.org/W2023206220', 'https://openalex.org/W2044681850', 'https://openalex.org/W2045528550', 'https://openalex.org/W2061932192', 'https://openalex.org/W2107839120', 'https://openalex.org/W2145700137', 'https://openalex.org/W2907627159'], 'related_works': ['https://openalex.org/W3184526518', 'https://openalex.org/W3133791286', 'https://openalex.org/W3127829407', 'https://openalex.org/W3100278686', 'https://openalex.org/W3094513761', 'https://openalex.org/W2983477422', 'https://openalex.org/W2969123634', 'https://openalex.org/W2963341998', 'https://openalex.org/W2963299623', 'https://openalex.org/W2952649849', 'https://openalex.org/W2949242690', 'https://openalex.org/W2740705535', 'https://openalex.org/W2577804023', 'https://openalex.org/W2527906400', 'https://openalex.org/W2362170751', 'https://openalex.org/W2149713202', 'https://openalex.org/W2016930771', 'https://openalex.org/W1978664187', 'https://openalex.org/W1631584060'], 'abstract_inverted_index': {'Results': [0], 'are': [1, 96, 101, 128, 143], 'obtained': [2], 'concerning': [3], 'the': [4, 24, 63, 69, 81, 114, 118, 124, 131], 'roots': [5, 85, 89, 142], 'of': [6, 10, 28, 47, 52, 67, 71, 74, 83, 105], 'asymmetric': [7, 147], 'geometric': [8, 26], 'representations': [9, 14], 'Coxeter': [11, 30, 115], 'groups.': [12, 42], 'These': [13, 99], 'were': [15], 'independently': [16], 'introduced': [17], 'by': [18, 90], 'Vinberg': [19], 'and': [20, 22, 79, 134], 'Eriksson,': [21], 'generalize': [23], 'standard': [25], 'representation': [27], 'a': [29, 34, 45, 49, 53, 58, 75, 91, 109, 136], 'group': [31, 92], 'in': [32, 62, 103], 'such': [33, 72], 'way': [35], 'as': [36], 'to': [37, 87, 113, 130, 135, 145], 'include': [38], 'all': [39], 'Kac--Moody': [40], 'Weyl': [41], 'In': [43], 'particular,': [44], 'characterization': [46], 'when': [48, 68, 80], 'non-trivial': [50], 'multiple': [51], 'root': [54, 59, 76], 'may': [55], 'also': [56, 97], 'be': [57], 'is': [60, 77, 94], 'given': [61], 'general': [64], 'context.': [65], 'Characterizations': [66], 'number': [70, 82], 'multiples': [73], 'finite': [78, 95], 'positive': [84, 141], 'sent': [86], 'negative': [88], 'element': [93], 'given.': [98], 'characterizations': [100], 'stated': [102], 'terms': [104], 'combinatorial': [106], 'conditions': [107], 'on': [108, 140], 'graph': [110, 116], 'closely': [111], 'related': [112], 'for': [117, 123], 'group.': [119], 'Other': [120], 'finiteness': [121], 'results': [122], 'symmetric': [125], 'case': [126], 'which': [127], 'connected': [129], 'Tits': [132], 'cone': [133], 'natural': [137], 'partial': [138], 'order': [139], 'extended': [144], 'this': [146], 'setting.': [148]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2800291541', 'counts_by_year': [{'year': 2018, 'cited_by_count': 2}], 'updated_date': '2024-12-12T09:53:49.809889', 'created_date': '2018-05-17'}