Kähler identities
= Kähler identities
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For the <Lefschetz operator of a Kähler manifold> and its adjoint, the Kähler identities include
$$
[\Lambda,\partial]=i\bar\partial^*,\qquad
[\Lambda,\bar\partial]=-i\partial^*,\qquad
[L,\partial^*]=i\bar\partial,\qquad
[L,\bar\partial^*]=-i\partial.
$$