Patience. It is actually diatoms and not algae at all. It is common in new tanks and eventually goes away with no action but it can take months. Meanwhile it wipes off easily when you scrape the glass. I used to take my rocks out periodically and scrub/soak them in hydrogen peroxide solution while I vacuumed the tank.
Diatoms are a type of algae.https://en.wikipedia.org/wiki/Diatom
Algae is an extremely general term. https://en.wikipedia.org/wiki/Algae Cyanobacteria could be excluded from the term algae by some definitions, though most often it is not, in common everyday usage of the term. I don't see the point of anybody in the aquarium hobby excluding it from the already extremely general term of algae just because it's a prokaryote. Just for example the fish food NLS algaemax advertises that it's got 7 types of algae.....they don't say it's got 6 types of algae plus 1 type of cyanobacteria. To exclude cyanobacteria from the already extremely general term algae, assumes that aquarists will have the ability to distinguish it. Their such a lack of quality information out there about all types of algae that it is virtually impossible for the average aquarist to become very knowledgeable about algae at all. I can't find the info to identify even one species of algae......only a vague idea of general grouping. I've been on fish forums for over 12 years now and have encountered at least 3 threads where people complimented the poster on how pretty their algae is, and IMO the algae in question is a type of cyanobacteria. And yes I'd agree the algae was very pretty, though I did not post to compliment them on their cyanobacteria. (Bright green with die off in round circles is an obvious tell tale sign). You, DJRansome, were amongst the posters complimenting the algae in at least 2 of these threads. No mention those times that it was not algae but cyanbacteria instead? The point being why do we want to try and make some major distinction for an already extremely general term when half the time many of us can't even tell the difference .....and virtually none of us could even identify one species of algae in our tanks!
Hydrogen peroxide might work on decor(?) Take it out of the tank and treat it. What i have found to work on Black brush Algae is simply a hot water soaking for about 20 minutes or so. As hot as what can come out of the tap is more then sufficient to zap it. I have tanks with either fiberglass or very thin sand and cement( bottoms, sides and back) and the black brush grows very thick and lush on bottom, back and sides and when it starts to cover all of the decor it far excedes the amount of alage i want in the tank. The decor blends in too much, especially the plastic plants and the tank lighting becomes too dim. I initially tried hydrogen peroxide and used hot water in the tub to rinse it off. The middle part of a 6 foot peice of driftwood had the algae come back almost instantly. Then I realized because the piece of driftwood was longer then the tub, the middle part did not get the hot water treatment. Anyways, a hot water treatment might be worth a try on decor that has diatoms, though I have no idea whether it will work as well on diatoms as it does on black brush algae.