You might be interested in the notion of a **braided Lie algebra** due to Majid. Roughly speaking this is a coalgebra ${L}$ in a braided category (ie $L$ is an object in a braided category category, with morphisms $\Delta:L \otimes L \to L$, and $\epsilon:L \to C$ satisfying the natural generalization of the axioms of a coalgebra), and in addition a morphism
$$
[ , ]:L \otimes L \to L,
$$
satisfying a "braided version" of the axioms of a Lie algebra.

The notion of the universal enveloping algebra of a Lie algebra generalizes to this context, and, quoting from Majid's paper http://arxiv.org/pdf/hep-th/9303148v1.pdf,

> ... the standard quantum deformations $U_q({\frak g})$ are understood
as the enveloping algebras of such underlying braided Lie algebras ...

A best place to learn about these structures is probably Majid's **Quantum Groups Primer** book

The paper [arxiv.org/abs/q-alg/9510004][1] mentioned in Jake's answer contains some discussion of these structures.


  [1]: http://arxiv.org/abs/q-alg/9510004%20a