Introduction. Let $k$ be a field of characteristic $0$, and let $n\in\mathbb N$. Let $V=k^n$. The group $\mathrm{GL}_n\left(k\right)=\mathrm{GL} V$ acts on $\mathrm{End} V$ by conj …

Question: Let $p$ be a prime. Let $k$ be a commutative ring such that $p=0$ in $k$. Let $\mathfrak g$ be an abelian $p$-restricted Lie algebra over $k$. In other words, let $\math …

Does there exist an integral domain $R$ and an $R$-module $M$ that is not flat over $R$ such that every tensor power of $M$ over $R$ is nonzero and $R$-torsion-free? (If such a do …

Question 1 (the weak and simple statement, which, I think, already is wrong): Let $p$ be a prime. Let $k$ be a field with characteristic $p$. For any $k$-vector space $V$, conside …

Suppose $V$ is a finite dimensional vector space of dimension n. What is the kernel of the map $$\bigwedge^p V \otimes \bigwedge^q V ----> \bigwedge^{p+q} V$$ ? (here $p+q< n …

We all know how to take integer tensor powers of line bundles. I claim that one should be able to also take fractional or even complex powers of line bundles. These might not be …