Before asking my question, a caveat: The category theorist in me would like me to ask this question in more generality, but I will restrict my scope since what I'm really after is …

Suppose that $A = \bigcup_{n=0}^{\infty} A_n$ is a filtered algebra over a field $k$. The associated graded algebra is $\mathrm{gr} A = \bigoplus_{n=0}^{\infty} A_n/A_{n-1}$, wher …

Hello! I've come across a lot of questions (and nice answers) on MO, concerning infinite-dimensional manifolds and differential calculus over them, but nothing suiting the simpler …

I ran across the following statement in a paper, and it seems fishy to me: Lemma: If $A$ is any Hopf algebra, and if $U$ is an $\mathbb{N}_0$-filtered $A$-module algebra, then $U …

Let $A$ be a comm. local $k$-algebra with max. ideal $m$. Let $gr(-)$ be the associated graded algebra or module for the $m$-adic filtration. The canonical derivation $d:A \to \O …