Abstract

AssumeTis a superstable theory with 0 is m-nonorthogonal to a *-algebraic type of-rank 1. We study the geometry induced by m-dependence on a *-algebraic typep*of-rank 1. We prove that after some localization this geometry becomes projective over a division ring. Associated withp*is a meager typep. We prove thatpis determined byp*up to nonorthogonality and thatunderlies also the geometry induced by forking dependence on any stationarization ofp. Also we study some *-algebraic *-groups of-rank 1 and prove that any *-algebraic *-group of-rank 1 is abelian-by-finite.