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The universal enveloping algebra $U(\mathfrak{tr}_n)$ of a Lie algebraassociated to the classical Yang-Baxter equation was introduced in [BEER06]where it was shown to be Koszul. This algebra appears as the $A_{n-1}$ case ina general class of braided Hopf algebras in [BB09] for any complex reflectiongroup. In this paper, we show that the algebras corresponding to the series$B_n$ and $D_n$, which are again universal enveloping algebras, are Koszul. Wefurther show how results of [BB09] can be used to produce pairs of adjointfunctors between categories of rational Cherednik algebra representations ofdifferent rank and type for the classical series of Coxeter groups.

Koszulness of Enveloping Algebras Associated to Generalized Yang-Baxter Equations