scholarly journals Koszul algebras and the quantum MacMahon master theorem

2007 ◽  
Vol 39 (4) ◽  
pp. 667-676 ◽  
Author(s):  
Phùng Hô Hai ◽  
Martin Lorenz
Keyword(s):  
Koszul Algebras ◽  
Master Theorem

scholarly journals COMBINATORICS AND N-KOSZUL ALGEBRAS

2008 ◽  
Vol 05 (08) ◽  
pp. 1205-1214
Author(s):  
ROLAND BERGER
Keyword(s):  
Hilbert Series ◽  
Natural Generalization ◽  
Koszul Algebras ◽  
Polynomial Algebras ◽  
New Type ◽  
Master Theorem

The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables. Furthermore, we present a new type of Hilbert series combinatorics, called comodule Hilbert series combinatorics, and due to Hai, Kriegk and Lorenz [15]. When the relations are all the antisymmetric tensors, a natural generalization of the MacMahon Master Theorem (MMT) is obtained from the comodule level, the original MMT corresponding to N = 2 and to polynomial algebras.

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

Discrete Koszul Algebras

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

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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