Hyperbolic and Metabolic Forms and Involutions

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Nokhodkar Hassan Abadi, Amir Hossein | 2014

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 45824 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Gholamzadeh Mahmoudi, Mohammad; Mahdavi-Hezavehi, Mohammad
Abstract:
In this thesis, we investigate the involutions of a Clifford algebra induced by involutions of orthogonal group in characteristic two. Several properties of these involutions, such as the relations between their invariants and their decompositions are studied. Also it is shown that a tensor product of quaternion algebras with involution can be expressed as the Clifford algebra of a suitable quadratic form with an involution induced by an involution of orthogonal group. Finally, in connection with the Pfister factor conjecture formulated by D. B. Shapiro, split tensor products of quaternion algebras with involution over a field of characteristic two are investigated
Keywords:
Clifford Algebra ; Quadratic Forms ; Involution ; Metabolic Form ; Hyperbolic Form ; Multiquaternion Algebra ; Orthogonal Group ; Orthogonal Symmetry