It's called a pan fixture. It would have had four cups (shade holders) hanging from the 4 arms.
I've never seen one with a "flat" glass shade for the main light. Usually they were rounded.
There are many examples of these in 2 arm, 3 and up to 5 arm...
They mostly dated from the late teens to the early '30's
I used to make reproductions of these (and early victorian chandeliers) and restored many of these pan fixtures in my day.
Here is just one example:
Vintage Brass Light Fixture with Original Shades from breadandbutter on Ruby Lane
Or, type in ~ antique brass pan ceiling light, in Google, then click on images....you'll see many differing kinds.