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Ted123
#3
Oct21-11, 04:28 PM
P: 449
Well the question I'm referring to is (in the context of lie algebras but similar for linear algebra): 'describe the kernel of the canonical homomorphism [itex]\phi : \mathfrak{g} \to \mathfrak{g} / \mathfrak{h}[/itex]' defined by [itex]\phi (x)=x+\mathfrak{h}[/itex] for all [itex]x\in\mathfrak{g}[/itex] where [itex]\mathfrak{g}[/itex] is any lie algebra (vector space with some additional properties) and [itex]\mathfrak{h}[/itex] is an ideal (subspace with some additional properties) of [itex]\mathfrak{g}[/itex].

I've found that [itex]\text{Ker}( \phi ) = \mathfrak{h}[/itex] but how would I present a basis?

What I mean by finding the kernel is using the definition [itex]\{ v\in V : \phi v)=0 \}[/itex]