Results

**1 - 3**of**3**### Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau Algebras with Skew PBW Extensions Algunas relaciones entre álgebras N-Koszul, Artin-Schelter regular y Calabi-Yau con extensiones PBW torcidas

"... Abstract Some authors have studied relations between Artin-Schelter regular algebras, N-Koszul algebras and CalabiYau algebras (resp. skew Calabi-Yau) of dimension d. In this paper we want to show through examples and counterexamples some relations between these classes of algebras with skew PBW ex ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract Some authors have studied relations between Artin-Schelter regular algebras, N-Koszul algebras and CalabiYau algebras (resp. skew Calabi-Yau) of dimension d. In this paper we want to show through examples and counterexamples some relations between these classes of algebras with skew PBW extensions. In addition, we also exhibit some examples of the preservation of these properties by Ore extensions. Key words: Skew PBW extensions, Calabi-Yau algebras, N-Koszul algebras, AS -regular algebras, Ore extensions. Resumen Algunos autores han estudiado las relaciones entre las álgebras Artin-Schelter regular, las álgebras N -Koszul y las álgebras Calabi-Yau (resp. skew Calabi-Yau) de dimensión d . En este artículo queremos mostrar a través de ejemplos y contraejemplos algunos relaciones entre estas clases de álgebras y las extensiones PBW torcidas. Además, mostraremos algunos ejemplos de preservación de estas propiedades en las extensiones de Ore.

### Contents

, 2014

"... We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi–Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametriz-ing such deformations has exactly six irreducible components, and we give explicit present ..."

Abstract
- Add to MetaCart

We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi–Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametriz-ing such deformations has exactly six irreducible components, and we give explicit presentations for the generic members of each family in terms of generators and relations. The proof uses deformation quantization to reduce the problem to a similar classification of unimodular quadratic Poisson structures in four dimensions, which we extract from Cerveau and Lins Neto’s classification of degree-two foliations on projective space. Corresponding to the “exceptional ” component in their classification is a quantization of the third symmetric power of the projective line that