2
votes
0answers
357 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
0answers
186 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
0answers
161 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
1answer
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
1answer
398 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
1answer
395 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
2answers
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
7answers
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
8answers
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., ...