In Manin's book: quantum groups and non-commutative geometry, there are two notations $A_q^{2|0}$ and $A_q^{0|2}$. Here $$ A_q^{2|0} = k<x,y>/(xy-q^{-1}yx), \\ A_q^{0|2} = k<\xi,\eta>/(\xi^2, \eta^2, \xi \eta + q \eta \xi). $$ Why he used $0, 2$? Are there some special meaning of $0, 2$? Is $A_q^{0|2}$ dual to $A_q^{2|0}$ is some sense? Thank you very much.
2026-03-26 04:32:07.1774499527
Notation $A_q^{2|0}$ and $A_q^{0|2}$ in Manin's book.
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