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Let $k$ be a field, $A$ a $k$-algebra, and $V$ a $k$-vector space. Then we can consider the representation varieties of $A$ on $V$: $\mathrm{Hom}_{k\textrm{-alg}}(A, \mathfrak{gl}(V))$ and $\mathrm{...

Let $k$ be a field, and let us write the "unadorned" tensor $\otimes$ in place of $\otimes_k$. For a unital finite-dimensional $k$-algebra $A$, let $A^e = A \otimes A^{op}$ denote the enveloping ...

Given a complex Lie algebra $\mathfrak g$, we can form its universal enveloping algebra and interpret it as a noncommutative space. Is this perspective useful? What does this space "look like"? How ...