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Untwisting a twisted CalabiYau algebra
"... Twisted CalabiYau algebras are a generalisation of Ginzburg’s notion of CalabiYau algebras. Such algebras A come equipped with a modular automorphism σ ∈ Aut(A), the case σ = id being precisely the original class of CalabiYau algebras. Here we prove that every twisted CalabiYau algebra may be ex ..."
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Twisted CalabiYau algebras are a generalisation of Ginzburg’s notion of CalabiYau algebras. Such algebras A come equipped with a modular automorphism σ ∈ Aut(A), the case σ = id being precisely the original class of CalabiYau algebras. Here we prove that every twisted CalabiYau algebra may be extended to a CalabiYau algebra. More precisely, we show that if A is a twisted CalabiYau algebra with modular automorphism σ, then the smash product algebras A ⋊σ N and A ⋊σ Z are CalabiYau.
Some Relations between NKoszul, ArtinSchelter Regular and CalabiYau Algebras with Skew PBW Extensions Algunas relaciones entre álgebras NKoszul, ArtinSchelter regular y CalabiYau con extensiones PBW torcidas
"... Abstract Some authors have studied relations between ArtinSchelter regular algebras, NKoszul algebras and CalabiYau algebras (resp. skew CalabiYau) 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 ..."
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Abstract Some authors have studied relations between ArtinSchelter regular algebras, NKoszul algebras and CalabiYau algebras (resp. skew CalabiYau) 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, CalabiYau algebras, NKoszul algebras, AS regular algebras, Ore extensions. Resumen Algunos autores han estudiado las relaciones entre las álgebras ArtinSchelter regular, las álgebras N Koszul y las álgebras CalabiYau (resp. skew CalabiYau) 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.
AMPLE GROUP ACTION ON ASREGULAR ALGEBRAS AND NONCOMMUTATIVE GRADED ISOLATED SINGULARITIES
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