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dc.contributor.advisorBerman, Stephenen_US
dc.creatorAzam, Saeiden_US
dc.date.accessioned2004-10-21T00:13:24Zen_US
dc.date.accessioned2013-01-04T05:04:10Z
dc.date.available1997-04-01T08:00:00Zen_US
dc.date.available2013-01-04T05:04:10Z
dc.date.created1997-04en_US
dc.date.issued1997-04-01en_US
dc.date.submittedApril 1997en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-10212004-001324en_US
dc.description.abstractThis thesis is about extended affine Lie algebras and extended affine Weyl groups. In Chapter I, we provide the basic knowledge necessary for the study of extended affine Lie algebras and related objects. In Chapter II, we show that the well-known twisting phenomena which appears in the realization of the twisted affine Lie algebras can be extended to the class of extended affine Lie algebras, in the sense that some extended affine Lie algebras (in particular nonsimply laced extended affine Lie algebras) can be realized as fixed point subalgebras of some other extended affine Lie algebras (in particular simply laced extended affine Lie algebras) relative to some finite order automorphism. We show that extended affine Lie algebras of type A1, B, C and BC can be realized as twisted subalgebras of types A§¤(l ¡Ã 2) and D algebras. Also we show that extended affine Lie algebras of type BC can be realized as twisted subalgebras of type C algebras. In Chapter III, the last chapter, we study the Weyl groups of reduced extended affine root systems. We start by describing the extended affine Weyl group as a semidirect product of a finite Weyl group and a Heisenberg-like normal subgroup. This provides a unique expression for the Weyl group elements which in turn leads to a presentation of the Weyl group, called a presentation by conjugation. Using a new notion, called the index, which is an invariant of the extended affine root systems, we show that one of the important features of finite and affine root systems (related to Weyl group) holds for the class of extended affine root systems. We also show that extended affine Weyl groups (of index zero) are homomorphic images of some indefinite Weyl groups where the homomorphism and its kernel are given explicitly.en_US
dc.language.isoen_USen_US
dc.subjectmathematicsen_US
dc.subjectLie algebraen_US
dc.subjectextended affine Lie algebrasen_US
dc.subjectextended affine Weyl groupsen_US
dc.subjectautomorphismen_US
dc.titleExtended affine lie algebras and extended affine weyl groupsen_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematics and Statisticsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US


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