Memorial University DAI: Group gradings on simple lie algebras of cartan and melikyan type

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Title	Group gradings on simple lie algebras of cartan and melikyan type
Author	McGraw, Jason Melvin
Description	Thesis (Ph.D.)--Memorial University of Newfoundland, 2010. Mathematics and Statistics
Date	2010
Pagination	vi, 91 leaves
Subject	Abelian groups; Automorphisms; Finite groups; Lie algebras;
Degree	Ph.D.
Degree Grantor	Memorial University of Newfoundland. Dept. of Mathematics and Statistics
Discipline	Mathematics and Statistics
Language	Eng
Notes	Includes bibliographical references (leaves 88-91)
Abstract	In 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).
Type	Text
Resource Type	Electronic thesis or dissertation
Format	Image/jpeg; Application/pdf
Source	Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries
Local Identifier	a3496973
Rights	The 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.
Collection	Electronic Theses and Dissertations
Scanning Status	Completed
PDF File	(9.04 MB) -- http://collections.mun.ca/PDFs/theses/McGraw_JasonMelvin.pdf
CONTENTdm file name	59217.cpd