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 …

Graded skew PBW extensions were defined by the first author as a generalization of graded
iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter …

In analogy with a recent result of N. Kowalzig and U. Krähmer for twisted Calabi–Yau
algebras, we show that the Hochschild cohomology ring of a Frobenius algebra with …

Some authors have studied relations between Artin-Schelter regular algebras, N-Koszul
algebras and Calabi-Yau algebras (resp. skew Calabi-Yau) of dimension d. In this paper we …

We describe the possible noncommutative deformations of complex projective three-space
by exhibiting the Calabi–Yau algebras that serve as their homogeneous coordinate rings …

Let A be a Koszul Artin–Schelter regular algebra and σ σ an algebra homomorphism from A
to M_ 2 * 2 (A) M 2× 2 (A). We compute the Nakayama automorphisms of a trimmed double …

Stefan and Guichardet have provided Lyndon–Hochschild–Serre type spectral sequences
which converge to the Hochschild cohomology and Ext groups of a smash product. We show …

Let R be an Artin-Schelter regular algebra and A= σ (R)(x1…, xn) be a graded quasi-
commutative skew PBW extension over R. In this paper we describe the Nakayama …

Nakayama automorphisms play an important role in the fields of noncommutative algebraic
geometry and noncommutative invariant theory. However, their computations are not easy in …

Let H be a Hopf algebra and A be an H-module algebra. This article investigates when the
smash product A] H is (skew) Calabi–Yau, has Van den Bergh duality or is Artin–Schelter …