# Tagged Questions

**2**

votes

**0**answers

444 views

### The link between the subfactors and the motives as enriched Galois theories?

On 29th March 2007, at the "École normale supérieure" of Paris, the mathematician Vaughan Jones, gave a conference (in French) entitled "Les sous-facteurs : une théorie de Galois enrichie" (see here), ...

**2**

votes

**0**answers

193 views

### How to determine there exists a unique invariant subspace for a set of matrices

Hi everyone,
Ive been looking at the following problem, but its not entirely in my area and some potential solutions seem to rely on algebraic geometry. Maybe thats just a complicated way to solve ...

**0**

votes

**0**answers

164 views

### abstract algebra for component wise operations on “vectors” or what it might be called

I have a quite tough problem to solve and need an algebra that allows to "vectors" following operations:
- multiplication between two vectors are componentwise that means v=(v1, v2, v3,...) multiplied ...

**1**

vote

**1**answer

84 views

### A set of vector such that any vector is orthogonal to to certain other vector (a generalization of the biorthogonal system of vectors))

We are given vectors $\mathbf a_1,\dots,\mathbf a_N\in\mathbb C^n$. Let these vectors be columns of $n$-by-N matrix $\mathbf A$. We additionally know that any $n-1$ vectors are linearly independent. ...

**3**

votes

**1**answer

413 views

### In quantum dynamical simulations, what is the symmetric (Riemannian) analog of a Poisson bracket?

The question narrowly posed is:
What is the accepted name of the bracket operation that is obtained by replacing the (antisymmetric) symplectic structure of the Poisson bracket with a (symmetric) ...

**5**

votes

**1**answer

403 views

### Log structure and degeneration

I am interested in compactification of the moduli space of elliptic curves, and I heard that Log geometry is very important for the problem.
I am developping the same technique for quantum geometry.
...

**1**

vote

**2**answers

143 views

### How to study the behavior of a particular function on a Vector Space.

Let, $V$ be a vector space over a field $K.$ Let, $T$ be a function from $V$ to $V$ such that
$T(kX) = kT(X)$ for all $k \in K$ and for all $X \in V$ and also
$T(k + X) = T(X)$ for all $k \in K$ ...

**30**

votes

**7**answers

3k views

### Why should algebraic objects have naturally associated topological spaces? (Formerly: What is a topological space?)

In this question, Harry Gindi states:
The fact that a commutative ring has a natural topological space associated with it is a really interesting coincidence.
Moreover, in the answers, Pete L. ...

**12**

votes

**8**answers

1k views

### Bimodules in geometry

Grothendieck's approach to algebraic geometry in particular tells us to treat all rings as rings of functions
on some sort of space. This can also be applied outside of scheme theory (e.g., ...