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 ...
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 ...
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. ...
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) ...
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. ...
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 $k \in K$ ...
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. ...
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., ...