All Questions

Suppose the base field algebraically closed and of zero characteristic. There are two fascinating questions in the intersection of ring theory and algebraic geometry (for which an excellent discussion ...

Let $ k $ be a field and $ A $ a connected graded $ k $-algebra ($ A $ is associative, but not assumed to be commutative). The algebra $ A $ is called Artin-Schelter Gorenstein* of dimension $ d $ if ...

Let $k$ be an algebraically closed field. Let $R := k\langle x,y \rangle/(yx-qxy) (q \in k^*)$. We often call $R$ a quantum plane. If $q$ is a primitive $n$-th root, then for any $(\zeta, \xi) \in k^* ...

A finite dimensional algebra (over $\mathbb{C}$, say) is said to be Frobenius if it comes equipped with a nondegenerate bilinear pairing \begin{align*} \langle -, - \rangle : A \times A \rightarrow \...