In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space g{\displaystyle {\mathfrak {g}}} together with a non-associative, alternating bilinear map g×g→g;(x,y)↦[x,y]{\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow {\mathfrak {g}};(x,y)\mapsto [x,y]}, called the Lie bracket, satisfying the Jacobi identity.