I'm reading the following motivation for studying quantum group but I'm unfamiliar with the double bracket notation in
$$U(\frak{g})[[\hbar]].$$
Is this a special set of polynomials with coefficient in the universal enveloping algebra of $\mathfrak{g}$?
2026-03-26 09:48:17.1774518497
What does the notation $U(\frak{g})[[\hbar]]$ mean?
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It denotes the formal power series ring with coefficients in the ring $U(\mathfrak{g})$. This is explicitly explained in texts on quantum groups, e.g., on page $2$ in the article Classification of quantum groups and Belavin–Drinfeld cohomologies.