In quantum case, we have commutators. In classical case, we have Poisson bracket. Let $T$ be a Poisson group, $a, b \in \mathbb{C}_q[T].$ It seems that we have $$ [a, b]=(q-1)\{a,b\}+o((q-1)^2). $$ Is this true? When $q\to 1$, we have $[a,b]/(q-1)\to \{a,b\}$.
2026-03-25 11:08:50.1774436930
Relation between Poisson bracket and commutator.
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