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I'm reading a paper and it says the following:

Let $K$ be a Lie group and fix an orthonormal framing $\{e_1, ..., e_n\}$ with respect to a left-invariant metric. This gives a splitting $$T^∗K = K × \mathbb R^n$$ which determines in an obvious way a hermitian almost complex structure and an invariant $(n, 0)$-form on teh cotangent bundle $T^*K$.

I see how we get the splitting of the cotangent bundle by taking the coframe, but I do not see how this immediately determines a hermitian almost complex structure and $(n,0)$-form.

Could someone point me in the right direction? Thanks.

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    The almost complex structure is on $T^*K$? $K$ might be odd dimensional – 2017-01-12
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    @JohnMa Yes, on $T^*K$. I've editted to make more clear. Thanks – 2017-01-20

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