  Following previous works for the unit ball, we define quasi-radial
pseudo-homogeneous symbols on the projective space and obtain the corresponding
commutativity results for Toeplitz operators. A geometric interpretation of
these symbols in terms of moment maps is developed. This leads us to the
introduction of a new family of symbols, extended pseudo-homogeneous, that
provide larger commutative Banach algebras generated by Toeplitz operators.
This family of symbols provides new commutative Banach algebras generated by
Toeplitz operators on the unit ball.
