{"id":"https://openalex.org/W106480167","doi":"https://doi.org/10.1007/978-3-642-40020-9_5","title":"Bi-invariant Means on Lie Groups with Cartan-Schouten Connections","display_name":"Bi-invariant Means on Lie Groups with Cartan-Schouten Connections","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W106480167","doi":"https://doi.org/10.1007/978-3-642-40020-9_5","mag":"106480167"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-40020-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40020-9_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-00846373","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003253553","display_name":"Xavier Pennec","orcid":"https://orcid.org/0000-0002-6617-7664"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210106545","display_name":"Research Centre Inria Sophia Antipolis - M\u00e9diterran\u00e9e","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Xavier Pennec","raw_affiliation_strings":["Asclepios Project-Team, INRIA Sophia-Antipolis M\u00e9diterran\u00e9e, 2004 Route des Lucioles, BP93, F-06902, Sophia Antipolis Cedex, France"],"affiliations":[{"raw_affiliation_string":"Asclepios Project-Team, INRIA Sophia-Antipolis M\u00e9diterran\u00e9e, 2004 Route des Lucioles, BP93, F-06902, Sophia Antipolis Cedex, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003253553"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210106545"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.33,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94132335,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"59","last_page":"67"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9767000079154968,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.9767000079154968,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9614999890327454,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.780437707901001},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5811951160430908},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.555195689201355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5535187125205994},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.4945809543132782},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.46381160616874695},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.4456753730773926},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4431781768798828},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.4305560290813446},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36711740493774414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3442879915237427},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.15873858332633972},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1563136875629425},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.15291860699653625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09896081686019897}],"concepts":[{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.780437707901001},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5811951160430908},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.555195689201355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5535187125205994},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.4945809543132782},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.46381160616874695},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.4456753730773926},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4431781768798828},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.4305560290813446},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36711740493774414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3442879915237427},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.15873858332633972},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1563136875629425},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.15291860699653625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09896081686019897},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-642-40020-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40020-9_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.3014","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.3014","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/84/63/73/PDF/GSI13_CartanConnections.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00846373v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00846373","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Geometric Science of Information (GSI 2013), Aug 2013, Paris, France. pp.59-67, ⟨10.1007/978-3-642-40020-9_5⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00846373v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00846373","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Geometric Science of Information (GSI 2013), Aug 2013, Paris, France. pp.59-67, ⟨10.1007/978-3-642-40020-9_5⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W606979596","https://openalex.org/W1492620113","https://openalex.org/W1579576867","https://openalex.org/W1598557217","https://openalex.org/W1632150706","https://openalex.org/W1667854146","https://openalex.org/W1767522689","https://openalex.org/W1777631236","https://openalex.org/W1969002377","https://openalex.org/W1983718735","https://openalex.org/W2017587562","https://openalex.org/W2029145515","https://openalex.org/W2040125300","https://openalex.org/W2048671095","https://openalex.org/W2059654406","https://openalex.org/W2067134006","https://openalex.org/W2069989676","https://openalex.org/W2072931016","https://openalex.org/W2079630523","https://openalex.org/W2109409043","https://openalex.org/W2128325826","https://openalex.org/W2134157700","https://openalex.org/W2162725890","https://openalex.org/W2201034663","https://openalex.org/W2245911421","https://openalex.org/W2610957222","https://openalex.org/W2617107436","https://openalex.org/W2741395613","https://openalex.org/W2951656971","https://openalex.org/W4211184603","https://openalex.org/W4242416715"],"related_works":["https://openalex.org/W4291625303","https://openalex.org/W3103229299","https://openalex.org/W2737579912","https://openalex.org/W3183653752","https://openalex.org/W4245686311","https://openalex.org/W4249424264","https://openalex.org/W2514150991","https://openalex.org/W2952578374","https://openalex.org/W4318710376","https://openalex.org/W3118825917"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}