{"id":"https://openalex.org/W1963918412","doi":"https://doi.org/10.1007/s002080010012","title":"Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms","display_name":"Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms","publication_year":2001,"publication_date":"2001-07-01","ids":{"openalex":"https://openalex.org/W1963918412","doi":"https://doi.org/10.1007/s002080010012","mag":"1963918412"},"language":"en","primary_location":{"id":"doi:10.1007/s002080010012","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002080010012","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069525654","display_name":"Hans Munthe\u2013Kaas","orcid":"https://orcid.org/0000-0002-4456-3150"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"H. Z. Munthe-Kaas","raw_affiliation_strings":["Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway hans@ii.uib.no, NO","Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway hans@ii.uib.no"],"affiliations":[{"raw_affiliation_string":"Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway hans@ii.uib.no, NO","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway hans@ii.uib.no","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067417848","display_name":"G. Quispel","orcid":"https://orcid.org/0000-0002-6433-1576"},"institutions":[{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"G. R. W. Quispel","raw_affiliation_strings":["Department of Mathematics La Trobe University Bundoora Melbourne 3083, Australia r.quispel@latrobe.edu.au, AU","Department of Mathematics La Trobe University Bundoora Melbourne 3083, Australia r.quispel@latrobe.edu.au"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics La Trobe University Bundoora Melbourne 3083, Australia r.quispel@latrobe.edu.au, AU","institution_ids":["https://openalex.org/I196829312"]},{"raw_affiliation_string":"Department of Mathematics La Trobe University Bundoora Melbourne 3083, Australia r.quispel@latrobe.edu.au","institution_ids":["https://openalex.org/I196829312"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015777960","display_name":"Antonella Zanna","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"A. Zanna","raw_affiliation_strings":["Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway anto@ii.uib.no, NO","Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway anto@ii.uib.no"],"affiliations":[{"raw_affiliation_string":"Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway anto@ii.uib.no, NO","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institutt for Informatikk University of Bergen H\u00f8yteknologisenteret Thorm\u00f8hlensgate 55 N-5020 Bergen, Norway anto@ii.uib.no","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069525654"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.6844,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.93203883,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":"3","first_page":"297","last_page":"324"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9983000159263611,"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/T10849","display_name":"Finite Group Theory Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.895438015460968},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.7430294752120972},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6542969942092896},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.630098283290863},{"id":"https://openalex.org/keywords/polar-decomposition","display_name":"Polar decomposition","score":0.6165295839309692},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5943588018417358},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.5495193004608154},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.5096783638000488},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.44196489453315735},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.44187667965888977},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.438763827085495},{"id":"https://openalex.org/keywords/lie-theory","display_name":"Lie theory","score":0.41277217864990234},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3417348265647888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2659352123737335},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2365177869796753},{"id":"https://openalex.org/keywords/adjoint-representation-of-a-lie-algebra","display_name":"Adjoint representation of a Lie algebra","score":0.21461552381515503},{"id":"https://openalex.org/keywords/lie-conformal-algebra","display_name":"Lie conformal algebra","score":0.1460733413696289}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.895438015460968},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.7430294752120972},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6542969942092896},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.630098283290863},{"id":"https://openalex.org/C130956294","wikidata":"https://www.wikidata.org/wiki/Q2101158","display_name":"Polar decomposition","level":3,"score":0.6165295839309692},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5943588018417358},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.5495193004608154},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.5096783638000488},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.44196489453315735},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44187667965888977},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.438763827085495},{"id":"https://openalex.org/C143135876","wikidata":"https://www.wikidata.org/wiki/Q357300","display_name":"Lie theory","level":5,"score":0.41277217864990234},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3417348265647888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2659352123737335},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2365177869796753},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.21461552381515503},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.1460733413696289},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s002080010012","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002080010012","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1981467185","https://openalex.org/W1983894121","https://openalex.org/W1984533458","https://openalex.org/W1990753794","https://openalex.org/W2055007784","https://openalex.org/W2061356302","https://openalex.org/W2088307891","https://openalex.org/W2105146991","https://openalex.org/W2120062331","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W4300900232","https://openalex.org/W2970628996","https://openalex.org/W1544488766","https://openalex.org/W592942203","https://openalex.org/W2038822312","https://openalex.org/W1571169080","https://openalex.org/W1982016221","https://openalex.org/W4367172905","https://openalex.org/W2057136683","https://openalex.org/W2037625254"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}