﻿ oipapio

### super algebra - Derivations of C(X)? or Why Must Supermanifolds be Smooth?

What are the derivations of the algebra of continuous functions on a topological manifold?A supermanifold is a locally ringed space (X,O) whose underlying space is a smooth manifold X, and whose sheaf of functions locally looks like a graded commutative algebra which is an exterior algebra over the sheaf of smooth functions. The wikipedia article has a detailed description. The n-lab post is a little thinner, but by pointing is out I've probably set in motion events that will alter it to be the superior article. Ahh, Heisenberg Uncertainty on t...Read more

### supermanifolds - How can I write down a point in the Berezinian of a super vector space?

A vector space \$V\$ of dimension \$n\$ has an associated determinant line \$Det(V)\$. An element of \$Det(V)\$ is represented as a (formal limear combination) of expresstions of the form \$v_1 \wedge v_2 \wedge \ldots \wedge v_n\$, subject to the usual multilinearity and antisymmetry relations.I'm wondering what is analog of the above fact/construction in the world of super vector spaces.Let \$V\$ be a supervector space of dimension \$n|m\$. Then there is a line \$Ber(V)\$ called the Berezinian of \$V\$, that behaves like a super-determinant.Here's a naive de...Read more