3 votes
Accepted

Fixed points of automorphism over quaternions

Multiplying on the right with $y$, we see that $x\in \mathbb{H}$ is a fixed point of $\rho_y$ iff $y\overline{x}=xy$. Case 1. $\overline{y}=-y$, i.e. the real part of $y$ vanishes so $y$ is pure ...
Joshua Tilley's user avatar
2 votes

representation for elements in $\pi_3(S^3)$

The answer is yes: Since quaternionic multiplication equips $S^3$ with an H-space structure, the sets $[X, S^3]_*$ inherit a multiplication (which we denote by $\mathbin{\cdot_{\mathbb{H}}}$) for all $...
Ben Steffan's user avatar
2 votes
Accepted

An example of local and global containments in quaternion algebras

Yes, this is a general fact that doesn't have to do with the fact that the quaternion algebra is ramified only at $p$--but I'm sure you have your reasons for that hypothesis! :) (I bet there's a ...
John Voight's user avatar
1 vote
Accepted

Calculating the class number of a maximal order from a Quaternion Algebra

Here is some Magma code to get you started: ...
John Voight's user avatar
1 vote

Finding all ideals of a prescribed norm in a quaternion order

This is an important point, so good that you are asking if you are confused! It's indeed explained in Lemma 17.6.1 which makes a forward reference to Lemma 26.4.1. I'll try to summarize the key ...
John Voight's user avatar
1 vote

Algorithm for determining if two ternary quadratic forms are similar

To check if two ternary quadratic forms over $\mathbb{Q}$ are similar over $\mathbb{Q}$, you can apply Theorem 5.1.1 and check instead either that the associated quaternion algebras are isomorphic (...
John Voight's user avatar

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