Publication Information

{'id': 'https://openalex.org/W1642864220', 'doi': None, 'title': 'C-Graded Vertex Algebras and their Representations', 'display_name': 'C-Graded Vertex Algebras and their Representations', 'publication_year': 2014, 'publication_date': '2014-01-01', 'ids': {'openalex': 'https://openalex.org/W1642864220', 'mag': '1642864220'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://escholarship.org/content/qt8x38x9qj/qt8x38x9qj.pdf?t=n8wkes', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', '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/A5036489243', 'display_name': 'Robert A. Laber', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Robert A. Laber', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5036489243'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 66}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', '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': 'Algebraic structures and combinatorial models', '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': 'Advanced Topics in Algebra', 'score': 0.9975, '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/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.992, '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/vertex-operator-algebra', 'display_name': 'Vertex operator algebra', 'score': 0.8984107}, {'id': 'https://openalex.org/keywords/operator-algebra', 'display_name': 'Operator algebra', 'score': 0.6522944}, {'id': 'https://openalex.org/keywords/operator-product-expansion', 'display_name': 'Operator product expansion', 'score': 0.5032205}], 'concepts': [{'id': 'https://openalex.org/C179724543', 'wikidata': 'https://www.wikidata.org/wiki/Q28509', 'display_name': 'Vertex operator algebra', 'level': 5, 'score': 0.8984107}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6738908}, {'id': 'https://openalex.org/C191413488', 'wikidata': 'https://www.wikidata.org/wiki/Q1892554', 'display_name': 'Operator algebra', 'level': 2, 'score': 0.6522944}, {'id': 'https://openalex.org/C80899671', 'wikidata': 'https://www.wikidata.org/wiki/Q1304193', 'display_name': 'Vertex (graph theory)', 'level': 3, 'score': 0.6133424}, {'id': 'https://openalex.org/C18199665', 'wikidata': 'https://www.wikidata.org/wiki/Q3883909', 'display_name': 'Operator product expansion', 'level': 2, 'score': 0.5032205}, {'id': 'https://openalex.org/C73648015', 'wikidata': 'https://www.wikidata.org/wiki/Q6543817', 'display_name': 'Lie conformal algebra', 'level': 3, 'score': 0.48548535}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.45257774}, {'id': 'https://openalex.org/C14394260', 'wikidata': 'https://www.wikidata.org/wiki/Q4723980', 'display_name': 'Algebra representation', 'level': 3, 'score': 0.3716427}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.33642113}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.3302575}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.32795897}, {'id': 'https://openalex.org/C100376341', 'wikidata': 'https://www.wikidata.org/wiki/Q649977', 'display_name': 'Jordan algebra', 'level': 4, 'score': 0.27788633}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, 'score': 0.057032168}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://escholarship.org/content/qt8x38x9qj/qt8x38x9qj.pdf?t=n8wkes', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W65708076', 'https://openalex.org/W590703233', 'https://openalex.org/W3138176368', 'https://openalex.org/W3105626800', 'https://openalex.org/W2963937182', 'https://openalex.org/W2772505091', 'https://openalex.org/W2601405806', 'https://openalex.org/W2397149581', 'https://openalex.org/W2301686278', 'https://openalex.org/W2167389927', 'https://openalex.org/W2125945495', 'https://openalex.org/W2092871383', 'https://openalex.org/W2059278097', 'https://openalex.org/W2045312509', 'https://openalex.org/W2023932340', 'https://openalex.org/W1825771386', 'https://openalex.org/W1802623620', 'https://openalex.org/W1626824608', 'https://openalex.org/W1599554001', 'https://openalex.org/W1534275946'], 'abstract_inverted_index': {'In': [0, 140], 'this': [1], 'thesis': [2], 'we': [3, 14, 69, 93, 160, 193], 'consider': [4, 15, 94], 'two': [5], 'related': [6], 'classes': [7], 'of': [8, 17, 35, 60, 73, 80, 100, 143, 181, 219, 232], 'vertex': [9, 21, 25, 67, 101, 109, 183, 189, 199, 204, 212, 222], 'algebras.': [10, 22, 103, 205], 'The': [11], 'first': [12], 'class': [13, 92], 'consists': [16], 'objects': [18], 'called': [19, 107], 'C-graded': [20, 66, 203], 'These': [23, 104], 'are': [24, 83, 106, 202], 'algebras': [26, 185, 201], 'with': [27, 39], 'additional': [28, 46], 'structure': [29, 47], 'that': [30, 53, 118, 162, 195, 209, 229], 'allows': [31], 'for': [32, 57, 148], 'the': [33, 51, 58, 61, 74, 87, 119, 141, 230], 'construction': [34, 59, 72], 'a': [36, 40, 65, 71, 78, 179, 187, 220], 'Zhu': [37, 62, 75], 'algebra': [38, 76, 214, 224], 'sufficiently': [41], 'well-behaved': [42], 'representation': [43], 'theory.': [44], 'This': [45], 'is': [48, 55, 117, 122, 129, 151, 225, 235], 'minimal': [49], 'in': [50], 'sense': [52], 'it': [54], 'necessary': [56], 'algebra.': [63], 'Given': [64], 'algebra,': [68, 191], 'provide': [70], 'and': [77, 112, 128, 192], 'pair': [79], 'functors': [81], 'which': [82, 227], 'inverse': [84], 'bijections': [85], 'between': [86], 'appropriate': [88], 'module': [89], 'categories.The': [90], 'second': [91], 'arises': [95], 'from': [96, 186], 'considering': [97], 'conformal': [98, 145, 217], 'deformations': [99], 'operator': [102, 110, 120, 184, 190, 200, 213, 223], 'structures': [105], 'pseudo': [108, 182, 198, 211], 'algebras,': [111], 'their': [113], 'main': [114], 'distinguishing': [115], 'feature': [116], 'L(0)': [121, 150, 166], 'not': [123, 152], 'assumed': [124], 'to': [125, 131, 154, 164, 167, 177], 'be': [126, 155, 168], 'semi-simple': [127, 156, 170], 'permitted': [130], 'have': [132, 137], 'complex': [133], 'eigenvalues.': [134], 'Similar': [135], 'theories': [136], 'been': [138], 'studied:': [139], 'context': [142], 'logarithmic': [144], 'field': [146], 'theory,': [147], 'example,': [149], 'required': [153], 'on': [157, 171], 'modules.': [158], 'Here,': [159], 'extend': [161], 'notion': [163], 'allow': [165], 'non': [169], 'V': [172], 'itself.': [173], 'We': [174, 206], 'show': [175], 'how': [176], 'construct': [178], 'family': [180], 'given': [188], 'prove': [194, 208], 'all': [196], 'such': [197], 'then': [207], 'every': [210], 'obtained': [215], 'via': [216], 'deformation': [218], 'lattice': [221], 'regular,': [226], 'means': [228], 'category': [231], 'admissible': [233], 'modules': [234], 'semi-simple.': [236]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1642864220', 'counts_by_year': [], 'updated_date': '2024-12-12T05:01:42.814916', 'created_date': '2016-06-24'}