Questions tagged [tensor-powers]

Let $V$ be an $R$-module. Traditionally the symmetric algebra $S(V)$ is defined as a quotient of the tensor algebra $T(V)$, by the ideal generated by all $a\otimes b-b\otimes a$. Can $S^n(V)$ also be ...

Given an algebra $A$ over $k$ with characteristic zero and a positive integer $n$, the subspace of $A^{\otimes n}$ consisting of all tensors invariant under the action of all permutations $\sigma\in\...

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 $p+q< n$) Thanks.. ...