Exceptional algebraic groups are divided into five types, namely G2, F4,E6, E7 and E8. In this thesis we discuss G2, F4 and E6. We discuss the exceptionalalgebraic groups via octonion algebras and Jordan algebras. We firstconsider the groups of type G2. Groups of type G2 are automorphism groupsof octonion algebras, a form of composition algebras. We take the algebra of Zorn vector matrices and find the possible values of automorphisms of thisalgebra with the help of U-operators. We also discuss the product of two andthree U-operators. Then we discuss Albert algebras, since groups of type E6and F4 are related to these algebras. The Albert algebras are a form of Jordanalgebras. We also study the U-operators in Albert algebras. In this thesis wework over algebraically closed fields of characteristic zero.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-488573 |
| Date | January 2022 |
| Creators | Ali, Hassan |
| Publisher | Uppsala universitet, Algebra, logik och representationsteori |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2022:41 |
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