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Centralizer

Centralizer[L, V]
gives the centralizer of the subset V in Lie algebra L.
  • The Lie algebra L and its subalgebras can be provided either from their structure constants or their infinitesimal generator representation. When providing the Lie algebra L with its structure constants denote the elements of the subspaces by using the symbol X, e.g. {X[1], X[4]}.
  • Let V be a subset of L. Then the set CL(V)={xL[x, v]=0 vV} is called the centralizer of V in L.
  • Centralizer returns the span of elements of L that make up the centralizer. Depending on the input, this can be given as a list of infinitesimal generators or by indexing the initial algebra using the symbol X.
  • The centralizer of the Lie algebra L is the center of L.
EXAMPLESCLOSE ALL
Basic Examples   (2)
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Let the Lie algebra:
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The centralizer of the subset spanned by {x, y, z} in L is:
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Let the Lie algebra:
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The centralizer of the subset spanned by the 5th and the 6th element of the algebra in L is:
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