With whom was Charlemagne’s empire divided? What are the reasons for the collapse of Charlemagne’s empire?

The empire of Charlemagne was divided among themselves by his grandchildren – Lothair (the ruler of the Rhine region, Frisia, Burgundy, and Northern Italy, who was de jure the emperor), Louis (the ruler of the German lands), and Charles the Bald (the territory of present-day France). The reason for the collapse of the state was the lack of economic and cultural ties between the regions, as well as the custom of dividing the property between the heirs.