Koszul and Gorenstein properties for homogeneous algebras

被引：45

作者：

Berger, Roland ^{[1
]}

Marconnet, Nicolas ^{[1
]}

机构：

[1] LARAL, Fac Sci & Tech, F-42023 St Etienne, France

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2006年 / 9卷 / 01期

关键词：

Koszul algebras; Gorenstein algebras; N-complexes; Hochschild (co) homology;

D O I：

10.1007/s10468-005-9002-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Koszul property was generalized to homogeneous algebras of degree N > 2 in [ 5], and related to N-complexes. We show that if the N-homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem to A, i.e., there is a Poincare duality between Hochschild homology and cohomology of A, as for N = 2.

引用

页码：67 / 97

页数：31

共 50 条

[31] Quadratic Gorenstein Rings and the Koszul Property II
Mastroeni, Matthew
Schenck, Hal
Stillman, Mike
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (02) : 1461 - 1482
[32] Notes on δ-Koszul Algebras
Lu, Jia-Feng
APPLIED CATEGORICAL STRUCTURES, 2012, 20 (02) : 143 - 159
[33] Discrete Koszul Algebras
Jia-Feng Lü
Miao-Sen Chen
Algebras and Representation Theory, 2012, 15 : 273 - 293
[34] Universally Koszul algebras
Conca, A
MATHEMATISCHE ANNALEN, 2000, 317 (02) : 329 - 346
[35] Koszul Algebras and Computations
Bigatti, Anna M.
De Negri, Emanuela
COMPUTATIONS AND COMBINATORICS IN COMMUTATIVE ALGEBRA, 2017, 2176 : 1 - 39
[36] Koszul algebras and their ideals
Piontkovskii, DI
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2005, 39 (02) : 120 - 130
[37] ON AN EXAMPLE OF δ-KOSZUL ALGEBRAS
Lue, Jia-Feng
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (11) : 3777 - 3781
[38] Notes on δ-Koszul Algebras
Jia-Feng Lü
Applied Categorical Structures, 2012, 20 : 143 - 159
[39] Yoneda algebras of almost Koszul algebras
Zheng Lijing
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2015, 125 (04): : 477 - 485
[40] GORENSTEIN DIMENSION AND AS-GORENSTEIN ALGEBRAS
Ueyama, Kenta
COMMUNICATIONS IN ALGEBRA, 2014, 42 (10) : 4253 - 4268

← 1 2 3 4 5 →