# Questions tagged [quaternions]

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### Why is the automorphism group of the octonions $G_2$ instead of $SO(7)$

I can calculate the derivation of the octonions and I clearly find the 14 generators that form the algebra of $G_2$. However, when I do the same calculation for the quaternions, I end up with the ...
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### Generalizing contour integration to quaternions and bicomplex numbers

I am interested in the possibility of generalizing the notion of contour integration to the quaternions or bicomplex numbers. I am aware that the Frobenius theorem prevents the construction of a true ...
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### Charaterisation of quaternion algebras

Let $k$ be a field, and $A$ an associative $k$-algebra with an identity element. Say that $A$ is quadratic if any subalgebra of $A$ generated by a single element has dimension at most two. I am ...
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There are all sorts of curios in low-dimensional Lie groups and Lie algebras, many of them due to the presence of the quaternions. There is, I have recently learned, an isomorphism $SO(6,2) \simeq SO(... 1answer 456 views ### Left- and right-sided principal ideals of quaternions have same index? One fact about the Lipschitz integers (quaternions of the form$a + bi + cj + dk$where$a, b, c, d$are integers) is that the left-sided ideal generated by any element$Q$has the same index in the ... 0answers 62 views ### 4-D lattices and quaternion It is easy to prove that there are only 2 extensions$\mathbb{Q}(a)$, with$|a|=1$, of$\mathbb{Q}$where$\mathbb{Z}[a]$becomes a lattice(discrete free abelian subgroup of rank 2) in the complex ... 0answers 208 views ### A Quaternions version of the Gauss Lucas theorem Edit: My serious thanks to Christian, Todd and Yemon for their comments to the previous version. The derivative is the same as Todd says:$(az^{n})'=naz^{n-1}$. The polynomial is in the form of$\...
For quaternionic hermitian matrices (i.e. quaternionic square matrices $(a_{ij})$ satisfying $a_{ji}=\bar a_{ij}$) there is a nice notion of (Moore) determinant which can be defined as follows. ...