In mathematics, a Lie algebra (pronounced LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an alternating bilinear map g × g → g {\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow {\mathfrak {g}}} , that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the Jacobi identity.
In mathematics, a Lie algebra (pronounced LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an alternating bilinear map g × g → g {\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow {\mathfrak {g}}} , that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the Jacobi identity.
Source: Wikipedia "Lie algebra" · CC BY-SA 4.0
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