Graded Calabi Yau Algebras of dimension 3

Hopf-Galois objects of Calabi-Yau Hopf algebras

By using the language of cogroupoids, we show that Hopf-Galois objects of a twisted Calabi-Yau Hopf algebra with bijective antipode are still twisted Calabi-Yau, and give their Nakayama automorphism explicitly. As applications, cleft Galois objects of twisted Calabi-Yau Hopf algebras and Hopf-Galois objects of the quantum automorphism groups of non-degenerate bilinear forms are proved to be twisted Calabi-Yau.

Calabi-Yau coalgebras

We provide a construction of minimal injective resolutions of simple comodules of path coalgebras of quivers with relations. Dual to Calabi-Yau condition of algebras, we introduce the Calabi-Yau condition to coalgebras. Then we give some descriptions of Calabi-Yau coalgebras with lower global dimensions. An appendix is included for listing some properties of cohom functors.

Skew Calabi-Yau property of normal extensions

We prove that the skew Calabi-Yau property is preserved under normal extension for locally finite positively graded algebras. We also obtain a homological identity which describes the relationship between the Nakayama automorphisms of skew Calabi-Yau locally finite positively graded algebras and their normal extensions. As a preliminary, we show that the Nakayama automorphisms of skew Calabi-Yau algebras always send a regular normal element to a multiple of itself by a unit.

A criterion for homogeneous potentials to be 3-Calabi-Yau

We give a necessary and sufficient condition for an N-Koszul algebra defined by a homogeneous potential, to be 3-Calabi-Yau. As an application, we recover two families of 3-Calabi-Yau algebras recently appeared in the literature, by studying skew polynomial algebras over non-commutative quadrics.

T-structures on a local 4-Calabi-Yau variety

Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize a large class of t-structures in the relevant Calabi-Yau category and try to calculate the combinatorics of them.

Cocommutative Calabi-Yau Hopf algebras and deformations

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra $\g$ with a finite subgroup $G$ of automorphisms of $\g$ is Calabi-Yau if and only if the universal enveloping algebra itself is Calabi-Yau and $G$ is a subgroup of the special linear group $SL(\g)$. The Noetherian cocommutative Calabi-Yau Hopf algebras of dimension not larger than 3 are describe…

Non-commutative projective Calabi-Yau schemes

The objective of the present article is to construct the first examples of (non-trivial) non-commutative projective Calabi-Yau schemes in the sense of Artin and Zhang.

非交换射影 Calabi-Yau 概形的若干例子

Some examples of noncommutative projective Calabi-Yau schemes

该研究借助非交换 Segre 积与量子加权超曲面构造非交换射影 Calabi-Yau 概形，并通过与交换情形及 Kanazawa 的例子比较，确认其中包含本质上的新例子。