quantum mechanics - What is the generator of an anti-unitary operator?

As the generator of a Unitary operator is a Hermitian operator, is the generator of an Anti-Unitary operator Anti-Hermitian?

Answer

I think you mean the following. Consider a (strongly continuous) one-parameter group of unitary operators $\mathbb R \ni t \mapsto U_t$. Then Stone's theorem implies that $$U_t= e^{itA}$$ for some self-adjoint operator $A$. Similarly, let $\mathbb R \ni t \mapsto U_t$ be a (strongly continuous) one-parameter group of anti-unitary operators. Is there a corresponding version of Stone's theorem where $$U_t= e^{itA}$$ for some antiself-adjoint operator $A$?

The answer is negative simply because it does not exist anything like a one-parameter group of anti-unitary operators. Since $U_t = U_{t/2}U_{t/2}$, every $U_t$ must be linear even if $U_{t/2}$ is antilinear (the product of two antilinear operators is linear).

This is the reason why antiunitary operators only describe discrete symmetries.