The use of superscripts in these formulas refers to elements of the dual algebra, and in particular that means that the map defined in the table is the dual coordinate map or Poincare duality map. More recently, others have introduced Hodge duality for very similar purposes – essentially the same formulas using subscripts instead of superscripts, so that the table refers to elements of a single algebra. You can read about this issue in more detail in this post on the bivector forum. Please post any further questions here.