Projective embeddings of dual polar spaces arising from a class of alternative division rings

We discuss some recent results of us regarding a class of polar spaces which includes the nonembeddable polar spaces introduced by Tits [Tits, J., “Buildings of spherical type and finite BN-pairs,” Lecture Notes in Mathematics 386, Springer-Verlag, Berlin-New York, 1974]. These results include an elementary construction of the polar space, a construction of a polarized embedding of the corresponding dual polar space and the determination whether this projective embedding is universal and unique (as a polarized embedding).