{"id":{"repo_id":"lancaster","oai_identifier":"oai:eprints.lancs.ac.uk:76230"},"canonical_url":"https://search.dev.ndltd.org/etd/lancaster/oai:eprints.lancs.ac.uk:76230","repository":{"repo_id":"lancaster","name":"Lancaster University","base_url":"https://eprints.lancs.ac.uk/cgi/oai2"},"display":{"title":"Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic","abstract":"Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component.","abstract_html":"Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component.","abstract_has_math":false,"creators":["Johnson, Heather","Levy, Paul","Towers, David"],"institution":"Lancaster University","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T02:48:24Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Johnson, Heather","Levy, Paul","Towers, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["Lancaster University"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics and Statistics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["Lancaster University"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.lancs.ac.uk/id/eprint/76230/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.lancs.ac.uk/id/eprint/76230/1/gap_code.zip","https://eprints.lancs.ac.uk/id/eprint/76230/2/2015johnsonphd.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component."]},{"key":"dc:format","label":"Dc Format","values":["application/zip","application/pdf"]},{"key":"dc:title","label":"Title","values":["Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic"]}]}],"canonical_facts":{"dc:creator":["Johnson, Heather","Levy, Paul","Towers, David"],"dc:date":["2015"],"dc:date.issued":["2015"],"dc:description.abstract":["Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component."],"dc:format":["application/zip","application/pdf"],"dc:identifier.uri":["https://eprints.lancs.ac.uk/id/eprint/76230/1/gap_code.zip","https://eprints.lancs.ac.uk/id/eprint/76230/2/2015johnsonphd.pdf"],"dc:publisher.commercial":["Lancaster University"],"dc:publisher.department":["Mathematics and Statistics"],"dc:publisher.institution":["Lancaster University"],"dc:relation.isreferencedby":["https://eprints.lancs.ac.uk/id/eprint/76230/"],"dc:title":["Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T02:48:24Z"}