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N-Koszul algebras, Calabi-Yau algebras and skew PBW extensions
(2017-11-01)
Abstract. In the schematic approach to non-commutative algebraic geometry arises some important classes of non-commutative algebras like Koszul algebras, Artin-Schelter regular algebras, Calabi-Yau algebras, and closely ...
Gelfand-kirillov dimension of skew pbw extensions
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 2013)
Gelfand-Kirillov dimension of Poincaré-Birkhoff-Witt (PBW for short) extensions was established by Matczuk ([15], Theorem A). Since PBW extensions are a particular example of skew PBWextensions (also called σ-PBW extensions), ...
Calabi-Yau property for graded skew PBW extensions
(Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas, 2017-07-01)
Graded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition ...
Valuations of skew quantum polynomials
(World Scientific, 2015-06)
In this paper, we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew Poincaré?Birkhoff?Witt (PBW) extensions. Moreover, we find a ...
Total Ring of fractions of skew PBW extensions
(2014)
We study the Gelfand Kirillov conjecture for some algebras and rings, we use similar tools for studying the ring of fractions of skew PBW extensions, establishing isomorphisms between algebras and rings. Particular cases ...
Interactions between non-commutative algebraic geometry and skew PBW extensions
(2016-08-11)
Abstract. We study some relations and interactions between non-commutative algebraic geometry and the skew PBW extensions. For this we will introduce a new class of noncommutative rings, the semi-graded rings, and for ...
Automorfismos de polinomios cuánticos torcidos
(2013)
En este trabajo estudiamos los automorfismos de extensiones PBW torcidas y polinomios cuánticos torcidos. Usando el trabajo de Artamonov como referencia se obtiene el resultado principal sobre automorfismos para extensiones ...
Projective modules and Gröbner bases for skew PBW extensions
(Polish Academy of Sciences. Institute of Mathematics, 2017-01)
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects ...
Maximality of noncommutative rings over orders
(Departamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2019-07-31)
La teoría de órdenes ha sido ampliamente estudiada desde la última parte del siglo XX. En el contexto no conmutativo, la maximalidad de órdenes ha sido revisada para objetos clásicos de tipo polinomial como las extensiones ...
Ideales primos en extensiones PBW torcidas
(2014)
En el trabajo estudiamos algunas propiedades de extensiones PBW torcidas, realizamos la construcción y caracterización por propiedad universal, describimos el proceso de extensión de ideales del anillo de coeficientes a ...