Affinizations and R-matrices for quiver Hecke algebras

Name: Work Video:
Duration: 3 min 30 s
Description: We introduce the notion of affinizations and R-matrices for arbitrary quiver Hekcke algebras. We show that they enjoy similar properties to those for symmetric quiver Hecke algebras. We next define the notion of a duality datum and construct a tensor functor between graded module categories of two quiver Hecke algebras. We give several examples of such functors .
Masaki Kashiwara; Euiyong Park
{'id': 'https://openalex.org/W335072090', 'doi': 'https://doi.org/10.48550/arxiv.1505.03241', 'title': 'Affinizations and R-matrices for quiver Hecke algebras', 'display_name': 'Affinizations and R-matrices for quiver Hecke algebras', 'publication_year': 2015, 'publication_date': '2015-01-01', 'ids': {'openalex': 'https://openalex.org/W335072090', 'doi': 'https://doi.org/10.48550/arxiv.1505.03241', 'mag': '335072090'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1505.03241', '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': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['arxiv', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/1505.03241', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5020587578', 'display_name': 'Masaki Kashiwara', 'orcid': 'https://orcid.org/0000-0001-6851-7581'}, 'institutions': [{'id': 'https://openalex.org/I125608817', 'display_name': 'Korea Institute for Advanced Study', 'ror': 'https://ror.org/041hz9568', 'country_code': 'KR', 'type': 'facility', 'lineage': ['https://openalex.org/I125608817']}], 'countries': ['KR'], 'is_corresponding': False, 'raw_author_name': 'Masaki Kashiwara', 'raw_affiliation_strings': ['Kyoto University, Japan and Korea Institute for Advanced Study, Seoul, Korea'], 'affiliations': [{'raw_affiliation_string': 'Kyoto University, Japan and Korea Institute for Advanced Study, Seoul, Korea', 'institution_ids': ['https://openalex.org/I125608817']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5066464361', 'display_name': 'Euiyong Park', 'orcid': 'https://orcid.org/0000-0002-5560-5387'}, 'institutions': [{'id': 'https://openalex.org/I124633538', 'display_name': 'University of Seoul', 'ror': 'https://ror.org/05en5nh73', 'country_code': 'KR', 'type': 'education', 'lineage': ['https://openalex.org/I124633538']}], 'countries': ['KR'], 'is_corresponding': False, 'raw_author_name': 'Euiyong Park', 'raw_affiliation_strings': ['University of Seoul, Republic of Korea'], 'affiliations': [{'raw_affiliation_string': 'University of Seoul, Republic of Korea', 'institution_ids': ['https://openalex.org/I124633538']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 6, 'citation_normalized_percentile': {'value': 0.852855, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 82, 'max': 83}, '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': 0.9994, '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': 'Nonlinear Waves and Solitons', 'score': 0.9986, '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/quiver', 'display_name': 'Quiver', 'score': 0.995257}, {'id': 'https://openalex.org/keywords/duality', 'display_name': 'Duality (order theory)', 'score': 0.45666745}, {'id': 'https://openalex.org/keywords/hecke-operator', 'display_name': 'Hecke operator', 'score': 0.42788178}], 'concepts': [{'id': 'https://openalex.org/C168310172', 'wikidata': 'https://www.wikidata.org/wiki/Q493980', 'display_name': 'Quiver', 'level': 2, 'score': 0.995257}, {'id': 'https://openalex.org/C156772000', 'wikidata': 'https://www.wikidata.org/wiki/Q864475', 'display_name': 'Functor', 'level': 2, 'score': 0.86950344}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.75840735}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7534188}, {'id': 'https://openalex.org/C2778023678', 'wikidata': 'https://www.wikidata.org/wiki/Q554403', 'display_name': 'Duality (order theory)', 'level': 2, 'score': 0.45666745}, {'id': 'https://openalex.org/C155281189', 'wikidata': 'https://www.wikidata.org/wiki/Q3518150', 'display_name': 'Tensor (intrinsic definition)', 'level': 2, 'score': 0.4518558}, {'id': 'https://openalex.org/C41217588', 'wikidata': 'https://www.wikidata.org/wiki/Q1592959', 'display_name': 'Hecke operator', 'level': 3, 'score': 0.42788178}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.41287225}, {'id': 'https://openalex.org/C75764964', 'wikidata': 'https://www.wikidata.org/wiki/Q870797', 'display_name': 'Modular form', 'level': 2, 'score': 0.08582312}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1505.03241', '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': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1505.03241', 'pdf_url': 'http://arxiv.org/pdf/1505.03241', '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': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1505.03241', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1505.03241', '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': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 11, 'referenced_works': ['https://openalex.org/W1604431959', 'https://openalex.org/W1672238818', 'https://openalex.org/W1988032111', 'https://openalex.org/W1990860481', 'https://openalex.org/W2027907621', 'https://openalex.org/W2149963522', 'https://openalex.org/W2963012673', 'https://openalex.org/W2963991109', 'https://openalex.org/W2964338259', 'https://openalex.org/W3098777676', 'https://openalex.org/W3104407645'], 'related_works': ['https://openalex.org/W4299849604', 'https://openalex.org/W4294660672', 'https://openalex.org/W3204951696', 'https://openalex.org/W3098444968', 'https://openalex.org/W2963815319', 'https://openalex.org/W2929154304', 'https://openalex.org/W2013109612', 'https://openalex.org/W1978933198', 'https://openalex.org/W1706072350', 'https://openalex.org/W1604812397'], 'abstract_inverted_index': {'We': [0, 13, 27, 50], 'introduce': [1], 'the': [2, 30], 'notion': [3, 31], 'of': [4, 32, 45, 54], 'affinizations': [5], 'and': [6, 36], 'R-matrices': [7], 'for': [8, 22], 'arbitrary': [9], 'quiver': [10, 24, 47], 'Hekcke': [11], 'algebras.': [12, 26, 49], 'show': [14], 'that': [15], 'they': [16], 'enjoy': [17], 'similar': [18], 'properties': [19], 'to': [20], 'those': [21], 'symmetric': [23], 'Hecke': [25, 48], 'next': [28], 'define': [29], 'a': [33, 38], 'duality': [34], 'datum': [35], 'construct': [37], 'tensor': [39], 'functor': [40], 'between': [41], 'graded': [42], 'module': [43], 'categories': [44], 'two': [46], 'give': [51], 'several': [52], 'examples': [53], 'such': [55], 'functors': [56], '.': [57]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W335072090', 'counts_by_year': [{'year': 2018, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 4}, {'year': 2015, 'cited_by_count': 1}], 'updated_date': '2024-12-14T21:58:41.398693', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
