# .

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.

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