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C3TorusCellStructure.png

C6TorusCellStructure.png

D6TorusCellStructure.png?

The original article:

• Harish-Chandra: On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc. 70 (1951) 28-96 [doi:10.1090/S0002-9947-1951-0044515-0]

Review:

• Eric Opdam, Valerio Toledano Laredo: On Harish-Chandra’s Isomorphism [arXiv:2412.17525]

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The quantum of magnetic flux is

$$\phi_0 \;=\; \frac{h}{e}$$

where

• $h$ is Planck's constant

• $e$ is the charge of the electron.

In SI units this is approximately

$$\phi_0 \;\equiv\; \frac{h}{e} \;\sim\; \frac {6.626 \times 10^{-34} \, J s} {1.602 \times 10^{-19} \, C} \;\sim\; 4.136 \times 10^{-15} \, \frac{J s}{C} \;=\; 4.136 \times 10^{-15} \, T m^2 \,,$$

where in the last step we used that

one Joule is one Newton meter

$$J \;=\; N m$$

and one Tesla is one Newton second per Coulomb meter

$$T \;\coloneqq\; \frac { N s } { C m } \,.$$

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• Aharonov–Bohm interference and fractional statistics in a quantum Hall interferometer

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 /

$D$

 /

$\partial$

New MathML code:

${\displaystyle D/}$

To test with with different browsers:

code	rendering
$\slash{D}$	$\slash{D}$
$D\!\!\!\!\!/$	$D\!\!\!\!\!/$
$𝐷̸$	$𝐷̸$
$\text{𝐷̸}$	$\text{𝐷̸}$
$\text{∂̸}$	$\text{∂̸}$

Testing MathML code directly:

$\stackrel{/}{D}$$\cancel{D}$

Combining Unicode characters:

D̸

d̸

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$$\underset{\mathbb{Z}}{\underbrace{ \pi_3(S^2) }} \longrightarrow \underset{\mathbb{Z}}{\underbrace{ \pi_2 \Omega S^2 }} \longrightarrow \pi_2 \mathcal{L} S^2 \longrightarrow \underset{\mathbb{Z}}{\underbrace{ \pi_2 S^2 }} \longrightarrow \underset{\mathbb{Z}}{\underbrace{ \pi_1 \Omega S^2 }} \xrightarrow{\phantom{-} \sim \phantom{-}} \underset{\mathbb{Z}}{\underbrace{ \pi_1 \mathcal{L} S^2 }}$$

$$0 \longrightarrow \mathbb{Z}/n \longrightarrow \pi_2 \mathcal{L} S^2 \longrightarrow \mathbb{Z} \longrightarrow 0$$