University of SaskatchewanHARVEST
  • Login
  • Submit Your Work
  • About
    • About HARVEST
    • Guidelines
    • Browse
      • All of HARVEST
      • Communities & Collections
      • By Issue Date
      • Authors
      • Titles
      • Subjects
      • This Collection
      • By Issue Date
      • Authors
      • Titles
      • Subjects
    • My Account
      • Login
      JavaScript is disabled for your browser. Some features of this site may not work without it.
      View Item 
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item

      Extended affine lie algebras and extended affine weyl groups

      Thumbnail
      View/Open
      NQ27440.pdf (6.883Mb)
      Date
      1997-04-01
      Author
      Azam, Saeid
      Type
      Thesis
      Degree Level
      Doctoral
      Metadata
      Show full item record
      Abstract
      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.
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Mathematics and Statistics
      Program
      Mathematics and Statistics
      Supervisor
      Berman, Stephen
      Copyright Date
      April 1997
      URI
      http://hdl.handle.net/10388/etd-10212004-001324
      Subject
      mathematics
      Lie algebra
      extended affine Lie algebras
      extended affine Weyl groups
      automorphism
      Collections
      • Graduate Theses and Dissertations
      University of Saskatchewan

      University Library

      © University of Saskatchewan
      Contact Us | Disclaimer | Privacy