Abstract
For (A, σ) a central simple algebra of even degree with orthogonal involution, we present a method for constructing isotropic right ideals in the even Clifford algebra (C 0(A, σ)σ) from isotropic right ideals in (A, σ). We then use this construction to fully describe the twisted flag varieties associated to algebraic groups of type D 4 (including the trialitarian groups).
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