Because there are three different minor scales, it is possible to come up with different sets of chords for a minor key by building chords on the notes of each different minor scale. Each variation to the notes of the scale alters the type of chords built on the scale.
The letter names of the chords remain the same, but the chord type may change. E.g. shown below are scale tone chords derived from the A harmonic minor scale. Notice that chord 3 is now augmented instead of major, and also that chord 5 is major instead of minor and chord 7 is diminished instead of major. These changes are all brought about by the raising of the 7th degree of the scale from G to G#.
This arpeggio based part uses chords derived from the A harmonic minor scale. Experiment with other ways of playing these chords and make up other progressions from them.