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**11**

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369 views

### Nullstellensatz for quaternionic plane curves?

By a quaternionic plane curve I mean the zero locus of a noncommutative polynomial in two variables, $x$ and $y$ say, over ${\Bbb H}$, Hamilton's quaternions. It is evidently well-known that, after ...

**10**

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526 views

### Quaternions: ellipse effect

I would be interested in an explanation of the "six ellipse effect" produced by the pseudocode below (I also wonder how close are these to being actual ellipses). Note the code is somewhat similar to ...

**9**

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381 views

### Polynomial function from $S^3$ to $S^3$ and quaternions

I am searching the polynomial functions from $S^3$ to $S^3$.
($S^3$ is the set of vectors $x$ in $\mathbb{R}^4$ such that $\|x\|=1$)
We say $g$ is a polynomial function from $S^3$ to $S^3$, if there ...

**8**

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135 views

### Determinants of octonionic hermitian matrices

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.
...

**4**

votes

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161 views

### Hochschild cohomology of SU(2)

I have a question about the computation of an Hochschild Cohomology. Or at least about a space which really looks like a cohomology space. All the functions i consider are assumed to be smooth.
Let's ...

**4**

votes

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97 views

### Grunsky-Motzkin-Schoenberg formula

I found this formula in Brian McCartin's interesting book "Mysteries of the equilateral triangle" http://www.kettering.edu/news/mysteries-equilateral-triangle and it looks as follows:
Suppose that $...

**3**

votes

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108 views

### Maximal compact subgroup of SL(2,|H)

The exceptional isomorphism $Spin(5,1)\simeq SL(2,\mathbb{H})$ is well-known, and I can find references that say the maximal compact of $Spin(5,1)$ is $Spin(5) \simeq Sp(2)$. So I know the answer to ...

**2**

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109 views

### Classification of symplectic representations of quaternion division algebras

I would like to know the classification of representations of the form $\rho:B^{\times}\to Sp(V,F)$ or ($Gsp(V)$), where $B$ is a quaternion division algebra over a number field $F$ (or $F=\mathbb{Q}$)...

**1**

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141 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 $\...

**1**

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94 views

### Does Feuter regularity imply derivability in all directions?

The standard type of regularity in Clifford Calculus is the one introduced by Feuter, namely:
a function is Feuter regular iff it is in the zero set of the Clifford-Dirac
operator $D= \...

**0**

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49 views

### How to take partial derivative of spherical interpolation of quaternions?

Using the standard definition of quaternionic spherical linear interpolation (slerp):
$$
Q(q_0,q_1,t) := q_0(q_0^{-1}q_1)^t,
$$
how can I take each partial derivative?
Actually, I'm confident how to ...

**0**

votes

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55 views

### Canonical forms of symmetric/skewsymmetric quaternionic matrix

$A$ belongs to $n$-dimensional quaternion symmetric matrix, in the sense that $A=A^T$, where $T$ means transpose. Under transformation $U$, $A\rightarrow U\cdot A\cdot U^T$, where $U$ is $n$-dim ...