#### DMCA

## AMPLE GROUP ACTION ON AS-REGULAR ALGEBRAS AND NONCOMMUTATIVE GRADED ISOLATED SINGULARITIES

### Citations

520 | Triangulated Categories in the Representation Theory ofFinite Dimensional Algebras - Happel - 1988 |

341 | Noncommutative noetherian rings - McConnell, Robson - 2001 |

187 | Cohen-Macaulay modules over Cohen-Macaulay rings, London Mathematical Society Lecture Note Series 146 - Yoshino - 1990 |

176 |
Noncommutative projective schemes
- Artin, Zhang
- 1994
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Citation Context ... ∗G)e) ∼= EndAG(A) as algebras in some nice situations (algebraic McKay correspondence). AMPLE GROUP ACTION ON AS-REGULAR ALGEBRAS 5 2. Ampleness We first review the notion of ampleness introduced in =-=[2]-=-. An algebraic triple (C,O, s) consists of a k-linear abelian category C, an object O ∈ C, and a k-linear autoequivalence s ∈ Autk C. Given a right noetherian graded algebra A, the noncommutative proj... |

120 | Y.: Mutation in triangulated categories and rigid Cohen-Macaulay modules - Iyama, Yoshino - 2008 |

36 | Growth of graded Noetherian rings - Stephenson, Zhang - 1997 |

34 | Skew group algebras in the representation theory of Artin algebras - Reiten, Riedtmann - 1985 |

18 | Stable categories of Cohen-Macaulay modules and cluster categories. arXiv:1104.3658 - Amiot, Iyama, et al. |

15 | Gourmet’s guide to Gorensteinness
- Jørgensen, Zhang
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Citation Context .... Since an AS-regular algebra S is a noncommutative generalization of a polynomial algebra, it is natural to study a fixed subalgebra SG of an AS-regular algebra S by a finite group G acting on S. In =-=[7]-=-, Jorgensen and Zhang introduced the notion of homological determinant for a graded algebra automorphism of S, which is the same as the usual determinant if S is a polynomial algebra generated in degr... |

9 | Tilting and cluster tilting for quotient singularities
- Iyama, Takahashi
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Citation Context ...nd G ≤ GL(d, k) a finite subgroup acting on S. The derived category Db(tails SG) and the graded stable category CMZ(SG) have been studied in two situations, namely, when S is generated in degree 1 in =-=[4]-=-, and when G = 〈diag(ξdeg x1 , . . . , ξdeg xd)〉 is a finite cyclic group where ξ ∈ k× is a primitive r-th root of unity so that SG = S(r) is the r-th Veronese algebra of S in [14] and [1, Section 5] ... |

9 | Skew Calabi-Yau Algebras and Homological Identities”, arXiv:1302.0437v2 [math.RA],
- Reyes, Rogalski, et al.
- 2013
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Citation Context ...s of finite length whose terms are finitely generated projectives. Extending the notion of Calabi-Yau algebra, the following class of algebras has been defined and studied in several literatures (see =-=[12]-=-). AMPLE GROUP ACTION ON AS-REGULAR ALGEBRAS 13 Definition 3.3. A graded algebra A is called graded skew bimodule Calabi-Yau of dimension d and of Gorenstein parameter ℓ if A ∈ perfZAe and RHomAe(A,A ... |

8 | The structure of AS-Gorenstein algebras,
- Minamoto, Mori
- 2011
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Citation Context ...linson algebra of S (Theorem 3.14). As a main ingredient of the proof, we also show that if S is a noetherian AS-regular algebra, then S ∗G is a noetherian AS-regular algebra over kG as introduced in =-=[9]-=- (Corollary 3.6). If G is ample, then SG is a graded isolated singularity, so the noncommutative projective scheme ProjSG associated to SG is smooth by definition. It follows that ProjSG itself is the... |

5 | Gorensteinness of invariant subrings of quantum algebras - Jing, Zhang - 1999 |

4 | Triangulated categories of Gorenstein cyclic quotient singularities
- Ueda
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Citation Context ...rated in degree 1 in [4], and when G = 〈diag(ξdeg x1 , . . . , ξdeg xd)〉 is a finite cyclic group where ξ ∈ k× is a primitive r-th root of unity so that SG = S(r) is the r-th Veronese algebra of S in =-=[14]-=- and [1, Section 5] (see [10] when S is AS-regular). One of the motivations of this paper is to integrate both situations to find a common theory. As one of such common theories, we show in this paper... |

1 |
McKay type correspondence for AS-regular algebras
- Mori
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Citation Context ... when G = 〈diag(ξdeg x1 , . . . , ξdeg xd)〉 is a finite cyclic group where ξ ∈ k× is a primitive r-th root of unity so that SG = S(r) is the r-th Veronese algebra of S in [14] and [1, Section 5] (see =-=[10]-=- when S is AS-regular). One of the motivations of this paper is to integrate both situations to find a common theory. As one of such common theories, we show in this paper that Db(ProjSG) := Db(tails ... |

1 |
Graded maximal Cohen-Macaulay modules over noncommutative graded Gorenstein isolated singularities
- Ueyama
(Show Context)
Citation Context ...ive) graded algebras, which agrees with the usual notion of isolated singularity if the algebra is commutative and generated in degree 1, and found some nice properties of such a class of algebras in =-=[15]-=-. This paper continues to study (noncommutative) graded isolated singularities. In commutative ring theory and representation theory of algebras, a fixed subalgebra SG of a polynomial algebra S = k[x1... |