Extended affine lie algebras and extended affine weyl groups

This 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 Aɩ (Ɩ ≥ 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.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor

University of Saskatchewan

Year dc:date.issued

1997

Author dc:creator

• Azam, Saeid

Advisor dc:contributor.advisor

• Berman, Stephen

• mathematics
• Lie algebra
• extended affine Lie algebras
• extended affine Weyl groups
• automorphism

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/10388/etd-10212004-001324

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/etd-10212004-001324