# Questions tagged [ade-classifications]

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12
questions

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votes

**1**answer

81 views

### dimension vector of indecomposable module over preprojective algebra

It is well-known that there are finitely many indecomposable module over the preprojective algebra associated to a quiver $Q$ if and only if $Q=A_2,A_3,A_4$ and tame type for $A_5$ and wild for others....

**11**

votes

**1**answer

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### equivariant stable class of quaternionic Hopf fibration in RO(G)-degrees of ADE-type

Does the quaternionic Hopf fibration possibly represent a non-torsion element in the $G$-equivariant stable homotopy groups of spheres, for $G$ a finite subgroup of $SO(3)$ and in RO(G)-degree being ...

**10**

votes

**2**answers

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### Symmetries of module categories over the category of representations of quantum $sl(2)$

The category $\mathcal{C}_l$ of tilting modules of the quantum group $U_q(sl_2)$ quotiented out by the modules of zero quantum dimension has a natural structure as a semisimple monoidal category when ...

**4**

votes

**1**answer

363 views

### Kodaira classification and the McKay correspondence

Kodaira's table of singular fibers has a singular fiber
for each of $\tilde{A}_n$, $\tilde{D}_n$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$; these are chains or cycles of (-2)-curves connected ...

**3**

votes

**0**answers

366 views

### Blowing up a projective surface

Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point, embed it in some projective space, and and consider a projection of it into $\mathbb{P}^3$. The ...

**10**

votes

**1**answer

1k views

### Du Val singularity of type G=A,D,E and “small” representations of G

We all know that a simple singularity $W_G(x_1,x_2,x_3)=0$ of type G=A,D,E has the following nice deformation involving the Cartan subalgebra $\mathfrak{h}$ of the Lie algebra $\mathfrak{g}$ of $G$. ...

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votes

**1**answer

387 views

### What is your favorite ADE-style classification? [duplicate]

Possible Duplicate:
ADE type Dynkin diagrams
What is your favorite ADE-style classification?
Here ADE style is to be understood in a very broad sense. A classification which is not precisely ...

**12**

votes

**2**answers

2k views

### Integral positive definite quadratic forms and graphs

Let me start with a question for which I know the answer. Consider a symmetric integral $n\times n$ matrix $A=(a_{ij})$ such that $a_{ii}=2$, and for $i\ne j$ one has $a_{ij}=0$ or $-1$. One can ...

**18**

votes

**4**answers

4k views

### Classification of finite groups of isometries

Consider the problem of classifying the finite groups of isometries of $\mathbb{R}^n$.
For $n=2$ it is cyclic and dihedral groups.
For $n=3$ they are well known, probably from Kepler and are related ...

**31**

votes

**1**answer

2k views

### Is there a common genesis for ADE classifications?

Recall that a certain type of object admits an ADE classification if there is a notion of equivalence relative to which equivalence classes of objects of the given type can be placed in one-to-one ...

**25**

votes

**1**answer

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### Does the quantum subgroup of quantum su_2 called E_8 have anything at all to do with the Lie algebra E_8?

The ordinary McKay correspondence relates the subgroups of SU(2) to the affine ADE Dynkin diagrams. The correspondence is that the vertices correspond to irreducible representations of the subgroup, ...

**29**

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**17**answers

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### ADE type Dynkin diagrams

The ADE type Dynkin diagrams seem to come up in seemingly different areas of math. Two places they come up are:
(1) Classification of simply laced complex simple lie algebras.
(2) Finite subgroups ...