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KillingForm

KillingForm[elem1, elem2]
gives the Killing form between two elements elemi of a linear Lie algebra.
KillingForm[L][baseElem1, baseElem2]
gives the Killing form of Lie algebra L between two base elements baseElemi.
KillingForm[L, {baseElem1, baseElem2}]
gives the Killing form of Lie algebra L between two base elements baseElemi.
  • The elements of the linear Lie algebra elemi are represented with matrices.
  • The Lie algebra L can be provided either from their structure constants or their infinitesimal generator representation. Depending on that, the resulting base elements baseElemi will be expresses either using the symbolic notation with X[i] denoting ith base element of the Lie algebra or by their infinitesimal generator representation and the symboli notation of the base elements.
  • The Killing form of a Lie algebra is the symmetric bilinear form K(X, Y)=Tr(ad X ad Y).
EXAMPLESCLOSE ALL
Basic Examples   (2)
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Let the Lie algebra:
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the following commands have the same effect, they give the killing form between the fist element of the chosen base for the Lie algebra
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Let the linear algebra
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the killing form between two elements of this Lie algebra is
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