Tag for quaternion algebras?

Question

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.

Answer 1

I agree with course of action (1): Expand the scope of quaternions to include quaternion algebras.

Partially because they are closely related, partially because this matches existing usage patterns, and partially because there are not enough questions of this type to merit a new tag.

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Completely as a side note, the preface to Hamilton's lectures on quaternions is well worth reading.

It's my opinion that the only reason modern readers ever find Hamilton's theoretical approach to quaternions difficult, is that they haven't really understood his theory of algebraic numbers first. That set of ideas is explained in his preface.

(The danger is to skim over the text because the equations look familiar. They might look familiar, but it's his interpretation that's unique.)

Answer 2

I agree with course of action (2): Create a new (quaternion-algebras) tag separate from the existing quaternions tag.

Expanding the existing quaternions tag is not suitable because most existing questions with this tag refer to the Hamiltonian quaternions, and often deal with interpreting Hamiltonian quaternions as rotations.

Answer 3

I agree with course of action (3): Do nothing.

There are not enough questions on this topic to merit a new tag and quaternion algebras are too different from the Hamiltonian quaternions for an expansion of the description for the quaternions tag.