Derivations of Group Algebras and Hochschild cohomology

Name: Work Video:
Duration: 3 min 30 s
Description: The Hochschild homology and cohomology group can be described in terms of the homology and cohomology of the classifying space of the groupoid of the adjoint action of the group under the suitable assumption of the finiteness of the supports of cohomology groups. The difference between homology and cohomology leads to a correction of the results in the book by D. J. Benson (1995),(1991).
Alina Mishchenko
{'id': 'https://openalex.org/W4289304836', 'doi': 'https://doi.org/10.48550/arxiv.1811.02439', 'title': 'Derivations of Group Algebras and Hochschild cohomology', 'display_name': 'Derivations of Group Algebras and Hochschild cohomology', 'publication_year': 2018, 'publication_date': '2018-01-01', 'ids': {'openalex': 'https://openalex.org/W4289304836', 'doi': 'https://doi.org/10.48550/arxiv.1811.02439'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1811.02439', '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/1811.02439', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5067470345', 'display_name': 'Alina Mishchenko', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Mishchenko, A. S.', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5067470345'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, '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': 62}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.9996, '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'}}, 'topics': [{'id': 'https://openalex.org/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.9996, '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'}}, {'id': 'https://openalex.org/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 0.999, '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'}}, {'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9988, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/hochschild-homology', 'display_name': 'Hochschild homology', 'score': 0.7901757}, {'id': 'https://openalex.org/keywords/mayer–vietoris-sequence', 'display_name': 'Mayer–Vietoris sequence', 'score': 0.68703806}, {'id': 'https://openalex.org/keywords/homology', 'display_name': 'Homology', 'score': 0.6564299}], 'concepts': [{'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.9302652}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8051319}, {'id': 'https://openalex.org/C2776648750', 'wikidata': 'https://www.wikidata.org/wiki/Q1622047', 'display_name': 'Hochschild homology', 'level': 3, 'score': 0.7901757}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.69312173}, {'id': 'https://openalex.org/C201595698', 'wikidata': 'https://www.wikidata.org/wiki/Q2421905', 'display_name': 'Mayer–Vietoris sequence', 'level': 5, 'score': 0.68703806}, {'id': 'https://openalex.org/C155751095', 'wikidata': 'https://www.wikidata.org/wiki/Q1408937', 'display_name': 'Group cohomology', 'level': 3, 'score': 0.6611984}, {'id': 'https://openalex.org/C165525559', 'wikidata': 'https://www.wikidata.org/wiki/Q224180', 'display_name': 'Homology (biology)', 'level': 3, 'score': 0.6564299}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.5458009}, {'id': 'https://openalex.org/C72738302', 'wikidata': 'https://www.wikidata.org/wiki/Q5384738', 'display_name': 'Equivariant cohomology', 'level': 3, 'score': 0.53757554}, {'id': 'https://openalex.org/C68365058', 'wikidata': 'https://www.wikidata.org/wiki/Q1179446', 'display_name': 'De Rham cohomology', 'level': 4, 'score': 0.41722602}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.41570243}, {'id': 'https://openalex.org/C184720557', 'wikidata': 'https://www.wikidata.org/wiki/Q7825049', 'display_name': 'Topology (electrical circuits)', 'level': 2, 'score': 0.32430166}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.16144398}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.08288586}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.07813516}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, '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://arxiv.org/abs/1811.02439', '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/1811.02439', 'pdf_url': 'http://arxiv.org/pdf/1811.02439', '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.1811.02439', '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/1811.02439', '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': [{'score': 0.46, 'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4297685638', 'https://openalex.org/W323070493', 'https://openalex.org/W3032867275', 'https://openalex.org/W2963483416', 'https://openalex.org/W2786552201', 'https://openalex.org/W2481546221', 'https://openalex.org/W2000421814', 'https://openalex.org/W1990583353', 'https://openalex.org/W192027584', 'https://openalex.org/W1644973113'], 'abstract_inverted_index': {'The': [0, 43], 'Hochschild': [1], 'homology': [2, 13, 46], 'and': [3, 14, 47], 'cohomology': [4, 15, 41, 48], 'group': [5, 29], 'can': [6], 'be': [7], 'described': [8], 'in': [9, 56], 'terms': [10], 'of': [11, 16, 20, 23, 27, 34, 37, 40, 53], 'the': [12, 17, 21, 24, 28, 31, 35, 38, 54, 57], 'classifying': [18], 'space': [19], 'groupoid': [22], 'adjoint': [25], 'action': [26], 'under': [30], 'suitable': [32], 'assumption': [33], 'finiteness': [36], 'supports': [39], 'groups.': [42], 'difference': [44], 'between': [45], 'leads': [49], 'to': [50], 'a': [51], 'correction': [52], 'results': [55], 'book': [58], 'by': [59], 'D.': [60], 'J.': [61], 'Benson': [62], '(1995),(1991).': [63]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4289304836', 'counts_by_year': [], 'updated_date': '2024-12-13T13:00:20.687524', 'created_date': '2022-08-02'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
