scholarly journals A GENERALIZED KOSZUL PROPERTY FOR SKEW PBW EXTENSIONS

2017 ◽  
Vol 101 (2) ◽  
pp. 301-320 ◽  
Author(s):  
Héctor Suárez ◽  
Armando Reyes
2016 ◽  
Vol 15 (03) ◽  
pp. 1650044
Author(s):  
András Magyar

The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symmetric special biserial algebras in terms of quivers and relations.


2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Luis Alfonso Salcedo Plazas

In this article we relate some Hopf algebra structures over Ore extensions and over skew PBW extensions ofa Hopf algebra. These relations are illustrated with examples. We also show that Hopf Ore extensions andgeneralized Hopf Ore extensions are Hopf skew PBW extensions.


Author(s):  
Yan Gu ◽  
Huy Tài Hà ◽  
Joseph W. Skelton

We show that attaching a whisker (or a pendant) at the vertices of a cycle cover of a graph results in a new graph with the following property: all symbolic powers of its cover ideal are Koszul or, equivalently, componentwise linear. This extends previous work where the whiskers were added to all vertices or to the vertices of a vertex cover of the graph.


2020 ◽  
Vol 30 (08) ◽  
pp. 1625-1650
Author(s):  
Oswaldo Lezama ◽  
Helbert Venegas

In this paper we compute the center of many noncommutative algebras that can be interpreted as skew [Formula: see text] extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.


2020 ◽  
Vol 48 (12) ◽  
pp. 5038-5055
Author(s):  
Arturo Niño ◽  
María Camila Ramírez ◽  
Armando Reyes

2013 ◽  
Vol 06 (04) ◽  
pp. 1350061 ◽  
Author(s):  
Oswaldo Lezama ◽  
Juan Pablo Acosta ◽  
Cristian Chaparro ◽  
Ingrid Ojeda ◽  
César Venegas

Many rings and algebras arising in quantum mechanics can be interpreted as skew Poincaré–Birkhoff–Witt (PBW) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others, are examples of skew PBW extensions. In this paper, we extend the classical Ore and Goldie theorems, known for skew polynomial rings, to this wide class of non-commutative rings. As application, we prove the quantum version of the Gelfand–Kirillov conjecture for the skew quantum polynomials.


2014 ◽  
Vol 6 (2) ◽  
pp. 233-259
Author(s):  
Dang Hop Nguyen
Keyword(s):  

2017 ◽  
Vol 39 (2) ◽  
pp. 181-203 ◽  
Author(s):  
Héctor Suárez ◽  
Armando Reyes
Keyword(s):  

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