The division-algebras tag has no usage guidance.

**12**

votes

**1**answer

982 views

### finite dimensional real division algebras

A celebrated theorem of Milnor and Kervaire asserts that any finite dimensional division algebra over the real numbers has dimension 1,2,4 or 8. This result is established using methods from algebraic ...

**3**

votes

**2**answers

735 views

### Skew fields inside quaternion division algebras

Suppose that $Q$ is a quaternion division algebra with center $k$, where $k$ is an arbitrary commutative field (let's say with $\operatorname{char}(k) \neq 2$ if necessary). Assume that $D$ is an ...

**14**

votes

**4**answers

1k views

### Dimension of central simple algebra over a global field “built using class field theory”.

If $F$ is a global field then a standard exact sequence relating the Brauer groups of $F$ and its completions is the following:
$$0\to Br(F)\to\oplus_v Br(F_v)\to\mathbf{Q}/\mathbf{Z}\to 0.$$
The ...

**-2**

votes

**4**answers

2k views

### Why don't quaternions have an overall phase? [closed]

The product of a quaternion multiplied by a real number is a quaternion, but the product of a quaternion multiplied by a complex number is not in general a quaternion. Why are the quaternions defined ...