Some Constructions of Bi-Koszul Algebras

2013 ◽  
Vol 20 (01) ◽  
pp. 141-154
Author(s):  
Junru Si ◽  
Jiafeng Lü
Keyword(s):  
Global Dimension ◽  
Koszul Algebras ◽  
Natural Question ◽  
Graded Algebras ◽  
Regular Algebras ◽  
Ore Extensions

Bi-Koszul algebras, including two classes of non-Koszul Artin-Schelter regular algebras of global dimension 4, were a class of graded algebras with non-pure resolutions, introduced in [8]. There is a natural question: can we construct bi-Koszul algebras from algebras with pure resolutions? In this paper, we study this question in terms of normal extensions and Ore extensions. More precisely, we attempt to obtain bi-Koszul algebras from algebras with pure resolutions by these two kinds of extensions. Furthermore, some homological properties of bi-Koszul algebras obtained in such ways are discussed.

scholarly journals GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS

2012 ◽  
Vol 55 (2) ◽  
pp. 241-257 ◽  
Author(s):  
IZURU MORI ◽  
KENTA UEYAMA
Keyword(s):  
Algebraic Geometry ◽  
Three Dimensional ◽  
Koszul Algebras ◽  
Graded Algebra ◽  
Graded Algebras ◽  
Regular Algebra ◽  
Morita Equivalent ◽  
Regular Algebras

AbstractClassification of AS-regular algebras is one of the major projects in non-commutative algebraic geometry. In this paper, we will study when given AS-regular algebras are graded Morita equivalent. In particular, for every geometric AS-regular algebra A, we define another graded algebra A, and show that if two geometric AS-regular algebras A and A' are graded Morita equivalent, then A and A' are isomorphic as graded algebras. We also show that the converse holds in many three-dimensional cases. As applications, we apply our results to Frobenius Koszul algebras and Beilinson algebras.

scholarly journals Algunas relaciones entre álgebras N-Koszul, Artin-Schelter regular y Calabi-Yau con extensiones PBW torcidas

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Héctor Suárez ◽  
O. Lezama ◽  
A. Reyes
Keyword(s):  
Koszul Algebras ◽  
Regular Algebras ◽  
Ore Extensions ◽  
Skew Pbw Extensions

<p>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 want to show through examples and counterexamples some relations between these classes of algebras with skew PBW extensions. In addition, we also exhibit some examples of the preservation of these properties by Ore extensions.</p>

scholarly journals Anick resolution and Koszul algebras of finite global dimension

2017 ◽  
Vol 45 (12) ◽  
pp. 5380-5383 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Soutrik Roy Chowdhury
Keyword(s):  
Global Dimension ◽  
Koszul Algebras ◽  
Finite Global Dimension

On graded algebras of global dimension 3

2001 ◽  
Vol 65 (3) ◽  
pp. 557-568 ◽  
Author(s):  
D I Piontkovskii
Keyword(s):  
Global Dimension ◽  
Graded Algebras

Graded Lie Algebras of Dimension Five and Some Artin–Schelter Regular Algebras

2019 ◽  
Vol 26 (02) ◽  
pp. 243-258
Author(s):  
Yuan Shen
Keyword(s):  
Lie Algebras ◽  
Global Dimension ◽  
Graded Lie Algebras ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Regular Algebras

In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. By parameterizing the relations of the universal enveloping algebras of three of those graded Lie algebras, we construct some new Artin–Schelter regular algebras of global dimension 5. We prove that those algebras are all strongly noetherian, Auslander regular and Cohen–Macaulay, and describe their Nakayama automorphisms.

A note on the global dimension of ore extensions

1969 ◽  
Vol 108 (4) ◽  
pp. 253-254 ◽  
Author(s):  
N. S. Gopala Krishnan
Keyword(s):  
Global Dimension ◽  
Ore Extensions

scholarly journals Noetherian Connected Graded Algebras of Global Dimension 3

2000 ◽  
Vol 230 (2) ◽  
pp. 474-495 ◽  
Author(s):  
Darin R. Stephenson ◽  
James J. Zhang
Keyword(s):  
Global Dimension ◽  
Graded Algebras

Some five-dimensional Artin–Schelter regular algebras obtained by deforming a Lie algebra

2016 ◽  
Vol 15 (04) ◽  
pp. 1650060 ◽  
Author(s):  
Jun Li ◽  
Xin Wang
Keyword(s):  
Lie Algebra ◽  
Global Dimension ◽  
Finite Dimensional ◽  
Regular Algebras ◽  
Graded Lie Algebra

We provide a class of Artin–Schelter regular algebras of global dimension 5 with four generators, which is obtained by parametrizing a finite-dimensional graded Lie algebra. Moreover, the algebras are piecewise-Koszul under a slight constraint on the parameters.

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