I am studying group theory by myself and while i was reading "Physics from symmetry", Jakob Schwichtenberg's book, he said it was conventional in physics to write the generators of SO(3) with an extra $i$, that is, multiplying the group generator matrix by $i$, but i am not understanding is why the generators have to be written like that? with the $i$, why this is conventional? what is the advantage?

In physics it’s conventional to define the generators of $SO ( 3)$ with an extra $i$. Concretely this means that instead of $e^{φ̃J}$ , we write $e^{iφJ}$ with with φ = − φ̃.

This is the quote that i am referring to in my question, right below equation 3.70, page 44.

I am studying group theory by myself and while i was reading "Physics from symmetry", Jakob Schwichtenberg's book, he said it was conventional in physics to write the generators of $SO(3)$ with an extra $i$, that is, multiplying the group generator matrix by $i$, but i am not understanding is why the generators have to be written like that? with the $i$, why this is conventional? what is the advantage?

In physics it’s conventional to define the generators of $SO ( 3)$ with an extra $i$. Concretely this means that instead of $e^{φ̃J}$ , we write $e^{iφJ}$ with with φ = − φ̃.

This is the quote that i am referring to in my question, right below equation 3.70, page 44.

I am studying group theory by myself and while i was reading "Physics from symmetry", Jakob Schwichtenberg's book, he said it was convetional in physics to write the generators of SO(3) with an extra "i", that is, multiplying the group generator matrix by i, but i am not understanding is why the generators have to be written like that? with the i, why this is convetional? what is the advantange?

In physics it’s conventional to define the generators of SO ( 3) with an extra "i". Concretely this means that instead of $e^{φ̃J}$ , we write $e^{iφJ}$ with φ = − φ̃.

This is the quote that i am refering to in my question, right below equation 3.70, page 44.

I am studying group theory by myself and while i was reading "Physics from symmetry", Jakob Schwichtenberg's book, he said it was conventional in physics to write the generators of SO(3) with an extra $i$, that is, multiplying the group generator matrix by $i$, but i am not understanding is why the generators have to be written like that? with the $i$, why this is conventional? what is the advantage?

In physics it’s conventional to define the generators of $SO ( 3)$ with an extra $i$. Concretely this means that instead of $e^{φ̃J}$ , we write $e^{iφJ}$ with with φ = − φ̃.

This is the quote that i am referring to in my question, right below equation 3.70, page 44.