0
votes
1answer
242 views

Domain of the wedge product in Little Spivak

Hello! in Little Spivak, p. 79, we find this: We will therefore define a new product, the wedge product $\omega\wedge\eta\in > \Lambda^{k+\ell}(V)$ by $$ > \omega\wedge\eta = > ...
6
votes
2answers
366 views

Generalized Grassmannians that parameterize the submodules of a module

I'm looking for something like a Grassmannian, but which parameterizes the submodules of a module rather than the subspaces of a vector space. Most specifically, I'm looking for something which ...
3
votes
1answer
181 views

Grassmannian as a submanifold of $\Lambda^m(E)$.

Let $E$ be a vector space of dimension $d\ge4$ over $K$, and $2\le m\le d$ be an integer. I am interested in the characterization of those elements $\omega$ of $\Lambda^m(E)$ that can be written in ...