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arXiv · 2507.10853

On differential smoothness of certain Artin-Schelter regular algebras of dimension 5

Andrés Rubiano
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Abstract

This article investigates the differential smoothness of various five-dimensional Artin-Schelter regular algebras. By analyzing the relationship between the number of generators and the Gelfand-Kirillov dimension, we provide structural obstructions to differential smoothness in specific algebraic families. In particular, we prove that certain two- and four-generator AS-regular algebras of global dimension five fail to admit a differential calculus, while a five-generator graded Clifford algebra provides a contrasting positive example.

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Andrés Rubiano. 2025-07-14. On differential smoothness of certain Artin-Schelter regular algebras of dimension 5. https://arxiv.org/abs/2507.10853

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