Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2745659389', 'doi': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'title': 'The structure of parafermion vertex operator algebras', 'display_name': 'The structure of parafermion vertex operator algebras', 'publication_year': 2009, 'publication_date': '2009-08-19', 'ids': {'openalex': 'https://openalex.org/W2745659389', 'doi': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'mag': '2745659389'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S184147796', 'display_name': 'Journal of Algebra', 'issn_l': '0021-8693', 'issn': ['0021-8693', '1090-266X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5103235948', 'display_name': 'Chongying Dong', 'orcid': 'https://orcid.org/0000-0003-3895-7951'}, 'institutions': [{'id': 'https://openalex.org/I24185976', 'display_name': 'Sichuan University', 'ror': 'https://ror.org/011ashp19', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I24185976']}, {'id': 'https://openalex.org/I185103710', 'display_name': 'University of California, Santa Cruz', 'ror': 'https://ror.org/03s65by71', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I185103710']}], 'countries': ['CN', 'US'], 'is_corresponding': True, 'raw_author_name': 'Chongying Dong', 'raw_affiliation_strings': ['Department of Mathematics, University of California, Santa Cruz, CA 95064, United States', 'School of Mathematics, Sichuan University, China'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics, Sichuan University, China', 'institution_ids': ['https://openalex.org/I24185976']}, {'raw_affiliation_string': 'Department of Mathematics, University of California, Santa Cruz, CA 95064, United States', 'institution_ids': ['https://openalex.org/I185103710']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5029578774', 'display_name': 'Ching Hung Lam', 'orcid': 'https://orcid.org/0000-0002-7583-1031'}, 'institutions': [{'id': 'https://openalex.org/I4210119858', 'display_name': 'National Center for Theoretical Sciences', 'ror': 'https://ror.org/02mfp0b67', 'country_code': 'TW', 'type': 'facility', 'lineage': ['https://openalex.org/I4210119858']}, {'id': 'https://openalex.org/I91807558', 'display_name': 'National Cheng Kung University', 'ror': 'https://ror.org/01b8kcc49', 'country_code': 'TW', 'type': 'education', 'lineage': ['https://openalex.org/I91807558']}], 'countries': ['TW'], 'is_corresponding': False, 'raw_author_name': 'Ching Hung Lam', 'raw_affiliation_strings': ['Department of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan 701'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan 701', 'institution_ids': ['https://openalex.org/I4210119858', 'https://openalex.org/I91807558']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5100434864', 'display_name': 'Qing Wang', 'orcid': 'https://orcid.org/0000-0002-8534-4077'}, 'institutions': [{'id': 'https://openalex.org/I191208505', 'display_name': 'Xiamen University', 'ror': 'https://ror.org/00mcjh785', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I191208505']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Qing Wang', 'raw_affiliation_strings': ['School of Mathematical Sciences, Xiamen University, Xiamen 361005, China'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematical Sciences, Xiamen University, Xiamen 361005, China', 'institution_ids': ['https://openalex.org/I191208505']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5053756860', 'display_name': 'Hiromichi Yamada', 'orcid': 'https://orcid.org/0000-0003-0883-2998'}, 'institutions': [{'id': 'https://openalex.org/I111428342', 'display_name': 'Hitotsubashi University', 'ror': 'https://ror.org/04jqj7p05', 'country_code': 'JP', 'type': 'education', 'lineage': ['https://openalex.org/I111428342']}], 'countries': ['JP'], 'is_corresponding': False, 'raw_author_name': 'Hiromichi Yamada', 'raw_affiliation_strings': ['Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan', 'institution_ids': ['https://openalex.org/I111428342']}]}], 'institution_assertions': [], 'countries_distinct_count': 4, 'institutions_distinct_count': 6, 'corresponding_author_ids': ['https://openalex.org/A5103235948'], 'corresponding_institution_ids': ['https://openalex.org/I24185976', 'https://openalex.org/I185103710'], 'apc_list': {'value': 3020, 'currency': 'USD', 'value_usd': 3020, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 2.376, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 63, 'citation_normalized_percentile': {'value': 0.973601, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 95, 'max': 96}, 'biblio': {'volume': '323', 'issue': '2', 'first_page': '371', 'last_page': '381'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10287', 'display_name': 'Cluster Algebras and Triangulated Categories', 'score': 1.0, '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'}}, 'topics': [{'id': 'https://openalex.org/T10287', 'display_name': 'Cluster Algebras and Triangulated Categories', 'score': 1.0, '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/T11673', 'display_name': 'Deformations and Structures of Hom-Lie Algebras', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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/T10248', 'display_name': 'Rogue Waves in Nonlinear Systems', 'score': 0.999, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/vertex-operator-algebra', 'display_name': 'Vertex operator algebra', 'score': 0.8789582}, {'id': 'https://openalex.org/keywords/kac-moody-algebras', 'display_name': 'Kac-Moody Algebras', 'score': 0.54476}, {'id': 'https://openalex.org/keywords/operator-algebra', 'display_name': 'Operator algebra', 'score': 0.48909432}, {'id': 'https://openalex.org/keywords/operator', 'display_name': 'Operator (biology)', 'score': 0.47141123}], 'concepts': [{'id': 'https://openalex.org/C179724543', 'wikidata': 'https://www.wikidata.org/wiki/Q28509', 'display_name': 'Vertex operator algebra', 'level': 5, 'score': 0.8789582}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.83480513}, {'id': 'https://openalex.org/C80899671', 'wikidata': 'https://www.wikidata.org/wiki/Q1304193', 'display_name': 'Vertex (graph theory)', 'level': 3, 'score': 0.6935007}, {'id': 'https://openalex.org/C191413488', 'wikidata': 'https://www.wikidata.org/wiki/Q1892554', 'display_name': 'Operator algebra', 'level': 2, 'score': 0.48909432}, {'id': 'https://openalex.org/C92757383', 'wikidata': 'https://www.wikidata.org/wiki/Q382497', 'display_name': 'Affine transformation', 'level': 2, 'score': 0.47628158}, {'id': 'https://openalex.org/C17020691', 'wikidata': 'https://www.wikidata.org/wiki/Q139677', 'display_name': 'Operator (biology)', 'level': 5, 'score': 0.47141123}, {'id': 'https://openalex.org/C81999800', 'wikidata': 'https://www.wikidata.org/wiki/Q1454725', 'display_name': 'Current algebra', 'level': 3, 'score': 0.44307488}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.43760428}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.39118242}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.38933998}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.36563364}, {'id': 'https://openalex.org/C100376341', 'wikidata': 'https://www.wikidata.org/wiki/Q649977', 'display_name': 'Jordan algebra', 'level': 4, 'score': 0.22433615}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, 'score': 0.04297051}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C158448853', 'wikidata': 'https://www.wikidata.org/wiki/Q425218', 'display_name': 'Repressor', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C86339819', 'wikidata': 'https://www.wikidata.org/wiki/Q407384', 'display_name': 'Transcription factor', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S184147796', 'display_name': 'Journal of Algebra', 'issn_l': '0021-8693', 'issn': ['0021-8693', '1090-266X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'https://arxiv.org/pdf/0909.3872v1.pdf', '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}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0904.2758', 'pdf_url': 'https://arxiv.org/pdf/0904.2758', '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': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jalgebra.2009.08.003', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S184147796', 'display_name': 'Journal of Algebra', 'issn_l': '0021-8693', 'issn': ['0021-8693', '1090-266X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 24, 'referenced_works': ['https://openalex.org/W1500962902', 'https://openalex.org/W1521327743', 'https://openalex.org/W1599554001', 'https://openalex.org/W1642629289', 'https://openalex.org/W1802623620', 'https://openalex.org/W1826377884', 'https://openalex.org/W1965482362', 'https://openalex.org/W1966976659', 'https://openalex.org/W1972876376', 'https://openalex.org/W1988167867', 'https://openalex.org/W1993624094', 'https://openalex.org/W2030200172', 'https://openalex.org/W2037658453', 'https://openalex.org/W2044715504', 'https://openalex.org/W2087474183', 'https://openalex.org/W2102571154', 'https://openalex.org/W2135410064', 'https://openalex.org/W2152507730', 'https://openalex.org/W2160087609', 'https://openalex.org/W2278590214', 'https://openalex.org/W2312591088', 'https://openalex.org/W2993697765', 'https://openalex.org/W3084323195', 'https://openalex.org/W338121346'], 'related_works': ['https://openalex.org/W4379135799', 'https://openalex.org/W2991580061', 'https://openalex.org/W2951020399', 'https://openalex.org/W2949912314', 'https://openalex.org/W2092871383', 'https://openalex.org/W2028773318', 'https://openalex.org/W1996022670', 'https://openalex.org/W1971089727', 'https://openalex.org/W1526788861', 'https://openalex.org/W1495441455'], 'abstract_inverted_index': {'It': [0], 'is': [1, 42], 'proved': [2], 'that': [3], 'the': [4, 11, 17, 37], 'parafermion': [5, 38], 'vertex': [6, 39], 'operator': [7, 40], 'algebra': [8, 20, 41], 'associated': [9], 'to': [10], 'irreducible': [12], 'highest': [13], 'weight': [14], 'module': [15], 'for': [16, 36], 'affine': [18], 'Kac–Moody': [19], 'A1(1)': [21], 'of': [22, 34], 'level': [23], 'k': [24], 'coincides': [25], 'with': [26], 'a': [27, 32], 'certain': [28], 'W-algebra.': [29], 'In': [30], 'particular,': [31], 'set': [33], 'generators': [35], 'determined.': [43]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2745659389', 'counts_by_year': [{'year': 2024, 'cited_by_count': 3}, {'year': 2023, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 5}, {'year': 2020, 'cited_by_count': 6}, {'year': 2019, 'cited_by_count': 6}, {'year': 2018, 'cited_by_count': 4}, {'year': 2017, 'cited_by_count': 11}, {'year': 2016, 'cited_by_count': 4}, {'year': 2015, 'cited_by_count': 2}, {'year': 2014, 'cited_by_count': 11}, {'year': 2013, 'cited_by_count': 3}], 'updated_date': '2024-09-18T22:12:51.860933', 'created_date': '2017-08-31'}