A crystal base for a representation of a quantum group on a Q ( v ) {\displaystyle \mathbb {Q} (v)} -vector space is not a base of that vector space but rather a Q {\displaystyle \mathbb {Q} } -base of L / v L {\displaystyle L/vL} where L {\displaystyle L} is a Q ( v ) {\displaystyle \mathbb {Q} (v)} -lattice in that vector space. Crystal bases appeared in the work of Kashiwara (1990) and also in the work of Lusztig (1990).
A crystal base for a representation of a quantum group on a Q ( v ) {\displaystyle \mathbb {Q} (v)} -vector space is not a base of that vector space but rather a Q {\displaystyle \mathbb {Q} } -base of L / v L {\displaystyle L/vL} where L {\displaystyle L} is a Q ( v ) {\displaystyle \mathbb {Q} (v)} -lattice in that vector space. Crystal bases appeared in the work of Kashiwara (1990) and also in the work of Lusztig (1990).
Source: Wikipedia "Crystal base" · CC BY-SA 4.0
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