# Gerasimovs theorem and N-Koszul algebras

## Related Articles

- Quasi- d-Koszul modules and applications. Jiafeng LÜ; Zhibing ZHAO // Chinese Annals of Mathematics;Jul2010, Vol. 31 Issue 4, p481
Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi- d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in...

- Graded algebras and their differential graded extensions. Piontkovski, D. // Journal of Mathematical Sciences;Apr2007, Vol. 142 Issue 4, p2267
In the survey, we deal with the following situation. Let A be a graded algebra or a differential graded algebra. Adjoining a set x of free (in any sense) indeterminates, we make a new differential graded algebra A< x> by setting the differential values d: x ? A on x. In the general case, such a...

- Algebras with periodic shifts of ext degrees. Jia-Feng Lü // Mathematical Notes;Dec2009, Vol. 86 Issue 5/6, p665
The so-called Î»-Koszul algebra and Î»-Koszul module are introduced. We give different equivalent descriptions of the Î»-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda Ext-algebra E( A) = âŠ• iâ‰¥0 Ext $$ \left( {\mathbb{F},\mathbb{F}} \right)...

- Inhomogeneous Yang-Mills Algebras. Berger, Roland; Dubois-Violette, Michel // Letters in Mathematical Physics;Apr2006, Vol. 76 Issue 1, p65
We determine all inhomogeneous Yangâ€“Mills algebras and super Yangâ€“Mills algebras which are Koszul. Following a recent proposal, a non-homogeneous algebra is said to be Koszul if the homogeneous part is Koszul and if the PBW property holds. In this letter, the homogeneous parts are...

- Koszul-like algebras and modules. Lü, Jia-Feng // Mathematical Notes;Mar2013, Vol. 93 Issue 3/4, p431
In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary...

- Linear Koszul duality, II: coherent sheaves on perfect sheaves. Mirković, I.; Riche, S. // Journal of the London Mathematical Society;Feb2016, Vol. 93 Issue 1, p1
In this paper we continue the study (initiated in a previous paper) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting and prove its compatibility with morphisms of vector...

- One-Point Extensions of t-Koszul Algebras. Zhi Cheng; Yu Ye // Acta Mathematica Sinica;Jun2007, Vol. 23 Issue 6, p965
We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras,...

- On Duality in the Homology Algebra of a Koszul Complex. Golod, E. // Journal of Mathematical Sciences;Aug2005, Vol. 128 Issue 6, p3381
The homology algebra of the Koszul complex K( x1, ..., x n; R) of a Gorenstein local ring R has Poincare duality if the ideal I = ( x1, ..., x n) of R is strongly Cohen-Macaulay (i.e., all homology modules of the Koszul complex are Cohen-Macaulay) and under the assumption that dim R - grade I...

- BMW ALGEBRA, QUANTIZED COORDINATE ALGEBRA AND TYPE C SCHURâ€“WEYL DUALITY. // Representation Theory;1/ 1/2011, Vol. 15, p1
The article presents a mathematical proof of an integral version of quantized type C Schurâ€“Weyl duality between the specialized Birmanâ€“Murakamiâ€“Wenzl algebra Bn(-q2m+1, q) and the quantum algebra associated to a symplectic Lie algebra sp2m. As stated, the quantized...