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A Lie algebra (pronounced as "lee") is an algebraic structure in mathematics whose main use lies in studying analytical objects such as Lie groups and differentiable manifolds. |
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A Lie algebra (pronounced as "lee") is an algebraic structure in mathematics whose main use lies in studying analytical objects such as Lie groups and differentiable manifolds. |
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If an algebra L with associative multiplication * is given, it can be turned into a Lie algebra by defining [x, y] = x * y - y * x. This expression is called the commutator of x and y. Conversely, it can be shown that every Lie algebra can be embedded into one that arises from an associative algebra in this fashion. |
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If an associative algebra L with multiplication * is given, it can be turned into a Lie algebra by defining [x, y] = x * y - y * x. This expression is called the commutator of x and y. Conversely, it can be shown that every Lie algebra can be embedded into one that arises from an associative algebra in this fashion. |
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