Most any copper based product will work to kill it (Copper safe Mardel labs etc, or dose with Blue stone and a test kit for Cu etc). Peroxide will also work.
You need to be careful not to over dose any of these.
You have a lot of light in there for a non planted tank.
If it's a BGA, you can simply do a large water change, Turn the lights out for about 3 days, clean your filters etc, pull the lights back away from the front of the glass.
I'd suggest you add some floating water sprite in there to suck up nutrients and add O2 and block the light so the algae are not are prevelant. Water sprite is hardy and does not need much, it'll be near the light, have some CO2 from the air above, all that's left are nutrients(NH4/NO3/PO4).
You can sell the excess. There some other suitable floating plants as well.
Cheaper and easier in the long run than copper, antibiotics, etc.
The other thing you can do is grow another desirable species of algae in specific locations. Pithophora is a beautiful velvet fur that will grow on wood and rocks, you need the rocks/wood near the surface and have high current and or aeration running across these surfaces.
This alga is non invasive and looks very nice and should keep other species at bay.
Since it is a SA/Ca tank, adding some Royal plecos/Blue eyes etc would be a nice addition and they will munch about anything and gnaw your wood.
So there are a number of suitable ideas for you.
Keeping up with large weekly water changes always solves most algae issues in Fish only tanks as well.
Regards,
Tom Barr