I ran across a reference to quantum algebra… WTF is quantum algebra?
I suppose the appropriate answer depends on whether you know what a Lie algebra is or not.
Assuming you do, quantum algebras are particular generalisations of the idea. The usual lingo is that you talk of deforming a Lie algebra, with this deformation characterised by a new parameter q. There will be a set of equations defining this algebra, that look pretty much like those for a Lie algebra, except that some of the terms depend on q. Things are set up in such a way that the limit q -> 1 recovers the Lie algebra you started from.
Basically the idea is that many of the “nice” properties of Lie algebras carry over to the generalisation. Much of the impetus in the field is mathematical physicists taking ideas - exactly solvable models and the like - that apply to Lie algebras and doing the q-algebra equivalent.
You’ll also see the term quantum group, which is just the q-equivalent of a Lie group.
If you don’t, then quantum algebras are just a fancy type of mathematical structure that have nice properties, allowing mathematical physicists to write lots of papers about them.
I’ve always thought the name slightly misleading. They have applications in areas of quantum physics, but you don’t get from “classical algebras” to quantum ones by “quantising” them. Unlike with quantum mechanics or quantum field theory.