A GENERALIZED KOSZUL PROPERTY FOR SKEW PBW EXTENSIONS

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.

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Hopf algebras and skew PBW extensions

CIENCIA EN DESARROLLO ◽

10.19053/01217488.v10.n2.2019.8797 ◽

2019 ◽

Vol 10 (2) ◽

Author(s):

Luis Alfonso Salcedo Plazas

Keyword(s):

Hopf Algebra ◽

Hopf Algebras ◽

Ore Extensions ◽

Skew Pbw Extensions

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.

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Projective modules and Gröbner bases for skew PBW extensions

Dissertationes Mathematicae ◽

10.4064/dm747-4-2016 ◽

2017 ◽

Vol 521 ◽

pp. 1-50 ◽

Cited By ~ 7

Author(s):

Oswaldo Lezama ◽

Claudia Gallego

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Projective Modules ◽

Skew Pbw Extensions

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Symbolic powers of cover ideals of graphs and Koszul property

International Journal of Algebra and Computation ◽

10.1142/s0218196721500405 ◽

2021 ◽

pp. 1-17

Author(s):

Yan Gu ◽

Huy Tài Hà ◽

Joseph W. Skelton

Keyword(s):

Vertex Cover ◽

Cycle Cover ◽

Symbolic Powers ◽

Koszul Property

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.

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Center of skew PBW extensions

International Journal of Algebra and Computation ◽

10.1142/s0218196720500575 ◽

2020 ◽

Vol 30 (08) ◽

pp. 1625-1650

Author(s):

Oswaldo Lezama ◽

Helbert Venegas

Keyword(s):

Polynomial Type ◽

Noncommutative Algebras ◽

Skew Pbw Extensions

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.

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Associated prime ideals over skew PBW extensions

Communications in Algebra ◽

10.1080/00927872.2020.1778012 ◽

2020 ◽

Vol 48 (12) ◽

pp. 5038-5055

Author(s):

Arturo Niño ◽

María Camila Ramírez ◽

Armando Reyes

Keyword(s):

Prime Ideals ◽

Associated Prime Ideals ◽

Skew Pbw Extensions ◽

Associated Prime

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ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS

Asian-European Journal of Mathematics ◽

10.1142/s1793557113500617 ◽

2013 ◽

Vol 06 (04) ◽

pp. 1350061 ◽

Cited By ~ 4

Author(s):

Oswaldo Lezama ◽

Juan Pablo Acosta ◽

Cristian Chaparro ◽

Ingrid Ojeda ◽

César Venegas

Keyword(s):

Commutative Rings ◽

Polynomial Rings ◽

Quantum Matrices ◽

Weyl Algebras ◽

Skew Polynomial Rings ◽

Finite Dimensional ◽

Quantum Version ◽

Skew Pbw Extensions ◽

Skew Polynomial ◽

Finite Dimensional Lie Algebras

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.

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