# Mathesis universalis

## More New Modules from Old

Publié dans Bible et nombres par mathesisuniversalis le avril 6, 2013

There are a few constructions we can make, starting with the ones from last time and applying them in certain special cases.

First off, if $latex V$ and $latex W$ are two finite-dimensional $latex L$-modules, then I say we can put an $latex L$-module structure on the space $latex \hom(V,W)$ of linear maps from $latex V$ to $latex W$. Indeed, we can identify $latex \hom(V,W)$ with $latex V^*\otimes W$: if $latex \{e_i\}$ is a basis for $latex V$ and $latex \{f_j\}$ is a basis for $latex W$, then we can set up the dual basis $latex \{\epsilon^i\}$ of $latex V^*$, such that $latex \epsilon^i(e_j)=\delta^i_j$.

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