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package org.jetbrains.kotlin.idea.refactoring.suggestions.library

import com.intellij.openapi.roots.impl.xml.XmlContent
import com.intellij.psi.PsiElement
import com.intellij.psi.PsiNamedElement
import com.intellij.psi.impl.PsiTreeUtil
import org.jetbrains.kotlin.descriptors.DescriptorsBinding
import org.jetbrains.kotlin.descriptors.KotlinBindingTarget
import org.jetbrains.kotlin.descriptors.common.BaseDescriptorsBinding
import org.jetbrains.kotlin.descriptors.generator.generateSubstituteWithDescriptorFor
import org.jetbrains.kotlin.descriptors.generator.generateSubstituteWithDescriptorSuffix
import org.jetbrains.kotlin.descriptors.generator.gener

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PasteBin.NET is not affiliated with the PasteBin source code repository for binary downloads. These binary downloads are provided by the PasteBin source code repository and/or their respective owners.Q:

Proof of Lie Algebra Commutator Identities

How would one go about proving these identities in the context of Lie algebra?

$[AB, C] = A [B, C] + B [A, C]$
$[C, AB] = – C [A, B]$
$\operatorname{ad}(A)^{ -1}(B) = – \frac{1}{2} \operatorname{ad}(A)[A,B] + A [B, A]$

Any guidance would be very helpful!

A:

This is to be accomplished by induction; the details are left to you.
Notice that $[X,Y] \in G$ and $[Y,X] \in G$ by the very definition of