Lie algebra homomorphism

Kernel of a Lie algebra homomorphism

The kernel ker⁡𝑓 of a Lie algebra homomorphism 𝑓 :𝔤 →𝔥 over a field 𝕂 is a special case of the kernel of an algebra homomorphism, #m/def/lie i.e. ker⁡𝑓 =𝑓−1{0}. It follows from the general case that the kernel is necessarily a Lie algebra ideal of 𝔤.

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