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Orthogonal symmetries and Clifford algebras
, Article Proceedings of the Indian Academy of Sciences: Mathematical Sciences ; Volume 120, Issue 5 , November , 2010 , Pages 535-561 ; 02534142 (ISSN) ; Sharif University of Technology
2010
Abstract
Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated
Hyperbolic and Metabolic Forms and Involutions
, Ph.D. Dissertation Sharif University of Technology ; Gholamzadeh Mahmoudi, Mohammad (Supervisor) ; Mahdavi-Hezavehi, Mohammad (Supervisor)
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