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Memorial University - Electronic Theses and Dissertations 4
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Document Description
TitleGroup gradings on simple lie algebras of cartan and melikyan type
AuthorMcGraw, Jason Melvin
DescriptionThesis (Ph.D.)--Memorial University of Newfoundland, 2010. Mathematics and Statistics
Paginationvi, 91 leaves
SubjectAbelian groups; Automorphisms; Finite groups; Lie algebras;
Degree GrantorMemorial University of Newfoundland. Dept. of Mathematics and Statistics
DisciplineMathematics and Statistics
NotesIncludes bibliographical references (leaves 88-91)
AbstractIn this thesis we explore the gradings by groups on the simple Cartan type Lie algebras and Melikyan algebras over algebraically closed fields of positive characteristic p > 2 (p = 5 for the Melikyan algebras). -- We approach the gradings by abelian groups without p-torsion on a simple Lie algebra L by looking at the dual group action. This action defines an abelian semisimple algebraic subgroup (quasi-torus) of the automorphism group of L. A result of Platonov says that any quasi-torus of an algebraic group is contained in the normalizer of a maximal torus. We show that if L is a simple graded Cartan or Melikyan type Lie algebra, then any quasi-torus of the automorphism group of L is contained in a maximal torus. Thus all gradings by groups without p-torsion are, up to isomorphism, coarsenings of the eigenspace decomposition of a maximal torus in the automorphism group. We also give examples of gradings by the cyclic group of order p which do not follow the pattern of the general description of gradings by groups without p-torsion as well as describe gradings by arbitrary groups on the restricted Witt algebra W(1; 1).
Resource TypeElectronic thesis or dissertation
FormatImage/jpeg; Application/pdf
SourcePaper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries
Local Identifiera3496973
RightsThe author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
CollectionElectronic Theses and Dissertations
Scanning StatusCompleted
PDF File(9.04 MB) --
CONTENTdm file name59217.cpd