On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Liu, L.-Y.

doi:10.1016/j.jalgebra.2017.11.034

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2022

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“…GWAs were introduced by Bavula [7] in early 1990s. Since then their structures and representations have been studied intensively, for example, their dimension and growth [8,10,9,55]; their derivations, isomorphisms and automorphisms [6,47,1,21,25]; and their homological and geometric properties [16,51,36,19,37,30].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

Zhao

2022

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We mainly study the growth and Gelfand-Kirillov dimension (GK-dimension) of generalized Weyl algebra (GWA) A = D(σ, a) where D is a polynomial algebra or a Laurent polynomial algebra. Several necessary and sufficient conditions for GKdim(A) = GKdim(D) + 1 are given. In particular, we prove a dichotomy of the GK-dimension of GWAs over the polynomial algebra in two indeterminates, namely, GKdim(A) is either 3 or ∞ in this case. Our results generalize several ones in the literature and can be applied to determine the growth, GK-dimension, simplicity, and cancellation properties of some GWAs.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

Zhao

2022

Preprint

View full text Add to dashboard Cite

show abstract

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

Zhao

2022

Sci. China Math.

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On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Cited by 2 publications

References 29 publications

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

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