In this paper we classify graded reflexive ideals, up to isomorphism and shift, in certain three-
dimensional Artin–Schelter regular algebras. This classification is similar to the classification …

We will prove a Riemann–Roch like theorem for triangulated categories satisfying Serre
duality. As an application, we will prove Riemann–Roch Theorem and Adjunction Formula …

We determine the possible Hilbert functions of graded rank one torsion free modules over
three dimensional Artin–Schelter regular algebras. It turns out that, as in the commutative …

We give a method for constructing maps from a non-commutative scheme to a commutative
projective curve. With the aid of Artin–Zhang's abstract Hilbert schemes, this is used to …

A Frobenius algebra over a field k is called symmetric if the Nakayama automorphism is an
inner automorphism. A stably symmetric algebra is defined to be a generalization of a …

In this paper, we will extend several results on intersection theory over commutative ruled
surfaces to quantum ruled surfaces. Typically, we define the fiber of a closed point, the quasi …

We compute the Grothendieck group K_0 of non-commutative analogues of quantum
projective space bundles. Our results specialize to give the Grothendieck groups of non …

The main aim of this paper is to discuss the relation between Serre's intersection multiplicity
and the Euler form. The Euler form is defined to be an alternating sum of the length of …

In the study of a finite dimensional hereditary algebra of infinite representation type,
understanding regular modules is essential. Recently, Herschend, Iyama and Oppermann …

This paper concerns an associative graded algebra A that is the enveloping algebra of a Lie
algebra with exponential growth. The algebra A is 3-Calabi-Yau. There is a Z-form of A so for …