A quaternion algebra is a generalization of the classical Hamiltonian quaternions. It is a $4$-dimensional algebra over a field $F$ with basis $1,i,j,ij$ subject to the relations $$ i^2 = a, \quad j^2 = b, \quad ji = -ij $$ for some $a,b \in F^\times$. (This is the definition for $\operatorname{char}(F) \neq 2$, anyway.)
There are quite a few questions on quaternion algebras, such as
Brauer Group of $\mathbb{Q}_2$
Proof that Quaternion Algebras are simple
Equivalent conditions of quaternion matrix algebra
Quaternion algebras over finite fields up to isomorphism
Quaternion algebra of characteristic 2?
Isomorphism of quaternion algebra
among others. Some of these posts are tagged with (quaternions), but according to its description the (quaternions) tag only seems to apply to the Hamilton quaternions:
For questions about the quaternions: a noncommutative four dimensional division algebra over the real numbers.
(The full description is here.) At the moment, there are 648 questions with a (quaternions) tag. Most probably refer to the Hamiltonian quaternions, but some (such as a couple of the above links) are about general quaternion algebras.
I see three possible courses of action:
(1) Expand the scope of the (quaternions) tag to include quaternion algebras.
(2) Create a new (quaternion-algebras) tag separate from the existing (quaternions) tag.
(3) Do nothing, if one thinks that there are not enough questions on this topic to merit a new tag and that quaternion algebras are too different from the Hamiltonian quaternions for an expansion of the existing tag description.
Which do you think is the best choice? I am leaning toward (2) because I get the sense that many questions with a (quaternions) tag are about interpreting Hamiltonian quaternions as rotations, while most questions about quaternion algebras relate to number theory.