scholarly journals On the Construction of d-Koszul algebras

2020 ◽  
pp. 243-249
Author(s):  
Ruaa Yousuf Jawad
Keyword(s):  
Koszul Algebras ◽  
Monomial Algebra

An algebra has been constructed from a (D, A)-stacked algebra A, under the conditions that , A 1 and . It is shown that when the construction of algebra B is built from a (D, A)-stacked monomial algebra A then B is a d-Koszul monomial algebra.

scholarly journals Koszul algebras and flow lattices

2022 ◽  
Vol 185 ◽  
pp. 105534
Author(s):  
Zsuzsanna Dancso ◽  
Anthony M. Licata
Keyword(s):  
Koszul Algebras

Koszul Algebras and Their Ideals

2005 ◽  
Vol 39 (2) ◽  
pp. 120-130 ◽  
Author(s):  
D. I. Piontkovskii
Keyword(s):  
Koszul Algebras

Homological Aspects of Semigroup Gradings on Rings and Algebras

1999 ◽  
Vol 51 (3) ◽  
pp. 488-505 ◽  
Author(s):  
W. D. Burgess ◽  
Manuel Saorín
Keyword(s):  
Euler Characteristic ◽  
Division Ring ◽  
Artinian Ring ◽  
Global Dimension ◽  
Monomial Algebra ◽  
Finite Dimensional ◽  
Cartan Matrices ◽  
Torsion Free ◽  
Rings And Algebras ◽  
Finite Dimensional Algebras

AbstractThis article studies algebras R over a simple artinian ring A, presented by a quiver and relations and graded by a semigroup Σ. Suitable semigroups often arise from a presentation of R. Throughout, the algebras need not be finite dimensional. The graded K0, along with the Σ-graded Cartan endomorphisms and Cartan matrices, is examined. It is used to study homological properties.A test is found for finiteness of the global dimension of a monomial algebra in terms of the invertibility of the Hilbert Σ-series in the associated path incidence ring.The rationality of the Σ-Euler characteristic, the Hilbert Σ-series and the Poincaré-Betti Σ-series is studied when Σ is torsion-free commutative and A is a division ring. These results are then applied to the classical series. Finally, we find new finite dimensional algebras for which the strong no loops conjecture holds.

Discrete Koszul Algebras

2010 ◽  
Vol 15 (2) ◽  
pp. 273-293 ◽  
Author(s):  
Jia-Feng Lü ◽  
Miao-Sen Chen
Keyword(s):  
Koszul Algebras

scholarly journals Comparison morphisms between two projective resolutions of monomial algebras

2017 ◽  
pp. 1-31
Author(s):  
María Julia Redondo ◽  
Lucrecia Román
Keyword(s):  
Lie Algebra ◽  
Hochschild Cohomology ◽  
Cohomology Groups ◽  
Efficient Tool ◽  
Simple Description ◽  
Monomial Algebra ◽  
Cup Product ◽  
Lie Bracket ◽  
Projective Resolutions ◽  
Bar Resolution

We construct comparison morphisms between two well-known projective resolutions of a monomial algebra $A$: the bar resolution $\operatorname{\mathbb{Bar}} A$ and Bardzell's resolution $\operatorname{\mathbb{Ap}} A$; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology $\operatorname{HH} ^*(A)$ and the second one has been shown to be an efficient tool for computation of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for $A= \mathbb{k} Q/I$ a monomial algebra such that $\dim_ \mathbb{k} e_i A e_j = 1$ whenever there exists an arrow $\alpha: i \to j \in Q_1$, we describe the Lie action of the Lie algebra $\operatorname{HH}^1(A)$ on $\operatorname{HH}^{\ast} (A)$.

scholarly journals On a class of Koszul algebras associated to directed graphs

2006 ◽  
Vol 304 (2) ◽  
pp. 1114-1129 ◽  
Author(s):  
Vladimir Retakh ◽  
Shirlei Serconek ◽  
Robert Lee Wilson
Keyword(s):  
Directed Graphs ◽  
Koszul Algebras

scholarly journals Koszul Algebras Defined by Three Relations

2017 ◽  
pp. 53-68 ◽  
Author(s):  
Adam Boocher ◽  
S. Hamid Hassanzadeh ◽  
Srikanth B. Iyengar
Keyword(s):  
Koszul Algebras
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