Anyonic Lie algebra

In mathematics, an anyonic Lie algebra is a U(1) graded vector space $L$ over $\mathbb{C}$ equipped with a bilinear operator $[-,-]$ and linear maps $\varepsilon\colon L\to\mathbb{C}$ and $\Delta\colon L \to L\otimes L$ satisfying

$\varepsilon([X,Y]) = \varepsilon(X)\varepsilon(Y)$

for pure graded elements X, Y, and Z.

References