I'm looking for a reference for the following fact. Suppose $A$ is a finitely generated associative commutative unital algebra over an algebraically closed field of characteristic …

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 …

Definition. Let $k$ be a commutative ring. Let $V$ be a $k$-module. We turn the symmetric algebra $\mathrm{S}\left(V\right)$ of $V$ into a graded Hopf algebra by defining the comul …

I have a category $C$, which is equipped with a symmetric monoidal structure (tensor product $\otimes$, unit object $1$). My category also has finite coproducts (I'll write them u …

Recall that for k a field, a finite dimensional k-algebra A is called symmetric if it is isomorphic to its dual as a bimodule of itself. Which is to say, there's a trace map t:A - …