{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/368142"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/368142","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras","abstract":"In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.","abstract_html":"In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.","abstract_has_math":false,"creators":["Faccin, Paolo"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-24T05:04:28Z","subjects":["Settore MAT/02 - Algebra"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_368142","10.15168/11572_368142"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_368142","href":"http://dx.doi.org/10.15168/11572_368142","code":true},{"text":"10.15168/11572_368142","href":"https://doi.org/10.15168/11572_368142","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11572/368142","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Faccin, Paolo"]},{"key":"dc:creator","label":"Author","values":["Faccin, Paolo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:89","numberofpages:89"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Settore MAT/02 - Algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11572/368142","http://dx.doi.org/10.15168/11572_368142","10.15168/11572_368142"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra."]},{"key":"dc:title","label":"Title","values":["Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras"]}]}],"canonical_facts":{"dc:contributor":["Faccin, Paolo"],"dc:creator":["Faccin, Paolo"],"dc:date":["2014"],"dc:description":["In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra."],"dc:identifier":["https://hdl.handle.net/11572/368142","http://dx.doi.org/10.15168/11572_368142","10.15168/11572_368142"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Trento","place:TRENTO"],"dc:relation":["firstpage:1","lastpage:89","numberofpages:89"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"dc:subject":["Settore MAT/02 - Algebra"],"dc:title":["Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:04:28Z"}