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date: 2022-02-12 21:07
modification date: Saturday 12th February 2022 21:07:16
title: SL2
aliases: [SL2]

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [ADE classification](ADE%20classification)
	- [simply laced](simply%20laced)
	- [loop algebra](loop%20algebra)
	- [Heisenberg algebra](Unsorted/superalgebra.md)
	- [Fock space](Fock%20space)

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# SL2

![](attachments/Pasted%20image%2020220424201006.png)

- Subgroups $G\subseteq \SL_2(\CC)$ are conjugate to subgroups of $\SU_2(\CC)$.
- There is a one-to-one correspondence between non-trivial finite subgroups $G$ of $S U(2)$ and the Dynkin diagrams $Q$ of types containing no double or triple edges:
	- $A_{n}(n \geq 1)$, 
	- $D_{n}(n \geq 4)$, 
	- $E_{6}$,
	- $E_{7}$,  
	- $E_{8}$

![](attachments/Pasted%20image%2020220410181022.png)