About: Complex Lie algebra

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In mathematics, a complex Lie algebra is a Lie algebra over the complex numbers. Given a complex Lie algebra , its conjugate is a complex Lie algebra with the same underlying real vector space but with acting as instead. As a real Lie algebra, a complex Lie algebra is trivially isomorphic to its conjugate. A complex Lie algebra is isomorphic to its conjugate if and only if it admits a real form (and is said to be defined over the real numbers).

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  • In mathematics, a complex Lie algebra is a Lie algebra over the complex numbers. Given a complex Lie algebra , its conjugate is a complex Lie algebra with the same underlying real vector space but with acting as instead. As a real Lie algebra, a complex Lie algebra is trivially isomorphic to its conjugate. A complex Lie algebra is isomorphic to its conjugate if and only if it admits a real form (and is said to be defined over the real numbers). (en)
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  • In mathematics, a complex Lie algebra is a Lie algebra over the complex numbers. Given a complex Lie algebra , its conjugate is a complex Lie algebra with the same underlying real vector space but with acting as instead. As a real Lie algebra, a complex Lie algebra is trivially isomorphic to its conjugate. A complex Lie algebra is isomorphic to its conjugate if and only if it admits a real form (and is said to be defined over the real numbers). (en)
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  • Complex Lie algebra (en)
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