  In the paper "Is there a Jordan geometry underlying quantum physics?" (Int.
J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective
geometries have been proposed as a framework for a geometric formulation of
Quantum Theory. In the present note, we refine this proposition by discussing
further structural features of Quantum Theory: the link with associative
involutive algebras, and with Jordan-Lie and Lie-Jordan algebas. The associated
geometries are (Hermitian) projective lines over an associative algebra; their
axiomatic definition and theory will be given in subsequent work with M.
Kinyon.
