Kana (nature and grace) as young Izanami (goddess of creation and death).
Alice in the Blue is inspired by a mix of Lewis Carroll's original novel, Alice in Wonderland, Alice Through the Looking Glass. and Japanese Shinto Mythology.
In Alice in the Blue Sky, The Chess Army has a system of ranking. Hierarchy is based on wisdom, strength, and element. The ranking is accurate to the actual rankings in the board game of Chess: Pawn, Rook, Knight, Bishop, Queen, and King (Champion). Alice begins her adventure as a pawn when she joins The White Chess army in the Sun Kingdom. She eventually works her way up to a Champion. The original novel Through the Looking Glass, in which Alice goes from being pawn to a queen, inspires this concept.
Myth:
“Tsukuyomi (God of the Moon) angered Amaterasu (Goddess of the Sun), when he killed Uke Mochi, the goddess of food. Amaterasu once sent Tsukuyomi to represent her at a feast presented by Uke Mochi. The goddess created the food by turning to the ocean and spitting out a fish, then facing a forest and spitting out game, and finally turning to a rice paddy and coughing up a bowl of rice. Tsukuyomi was utterly disgusted by the fact that, although it looked exquisite, the meal was made in a disgusting manner, and so he killed her. Soon, Amaterasu learned what happened and she was so angry that she refused to ever look at Tsukuyomi again, forever moving to another part of the sky. This is the reason that day and night are never together” (Wikipedia).
Based on Shinto Mythology, the war between the White Chess and the Black Chess is a representation of the gods of the Sun and Moon.