There are two aspects to this survey. First, in Sections 1-3 we give an introduction to the
main ideas and fundamental results in the theory of Artin-Schelter regular algebras, suitable …

In establishing a more general version of the McKay correspondence, we prove Auslander's
theorem for actions of semisimple Hopf algebras H on noncommutative Artin–Schelter …

We introduce the notion of quantum-symmetric equivalence of two connected graded
algebras, based on Morita–Takeuchi equivalences of their universal quantum groups, in the …

Let A=⊕ n= 0∞ A n be a connected graded k-algebra over an algebraically closed field k
(thus A 0= k). Assume that a finite Abelian group G, of order coprime to the characteristic of k …

Let E be an elliptic curve defined over an algebraically closed field k whose characteristic is
not 2 or 3. Let τ be a translation automorphism of E that is not of order 2. In a previous paper …

We examine the relationship between certain noncommutative analogues of projective 3-
space, ℙ 3, and the quantized enveloping algebras U q (sl 2). The relationship is mediated …

We study cocycle twists of a 4-dimensional Sklyanin algebra A and a factor ring B which is a
twisted homogeneous coordinate ring. Twisting such algebras by the Klein four-group G, we …

The attempted classification of regular algebras of global dimension four, so-called quantum
P³s, has been a driving force for modern research in noncommutative algebra. Inspired by …

We introduce a new method to construct 4-dimensional Artin-Schelter regular algebras as
normal extensions of (not necessarily noetherian) 3-dimensional ones. The method …

Let $ R $ denote a 6-dimensional subspace of the ring $ M_4 (\Bbbk) $ of $4\times 4$
matrices over an algebraically closed field $\Bbbk $. Fix a vector space isomorphism $ M_4 …