# Anyonic Lie algebra

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