  A theory of canonical basis for a two-parameter quantum algebra is developed
in parallel with the one in one-parameter case. A geometric construction of the
negative part of a two-parameter quantum algebra is given by using mixed
perverse sheaves and Deligne's weight theory based on Lusztig's work. A
categorification of the negative part of a two-parameter quantum algebra is
provided. A two-parameter quantum algebra is shown to be a two-cocycle
deformation, depending only on the second parameter, of its one-parameter
analogue.
