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arXiv · 2201.03167

Generalized Down-up Algebras Revisited from A Viewpoint of Gr\"obner Basis Theory

Rabigul Tuniyaz·Gulshadam Yunus
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Abstract

The so called generalized down-up algebras are revisited from a viewpoint of Gr\"obner basis theory. Particularly it is shown explicitly that generalized down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne 0$), and by means of homogeneous Gr\"obner defining relations, the associated graded structures of generalized down-up algebras, namely the associated graded algebras, Rees algebras, and the homogenized algebras of generalized down-up algebras, are explored comprehensively.

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Rabigul Tuniyaz, Gulshadam Yunus. 2022-01-10. Generalized Down-up Algebras Revisited from A Viewpoint of Gr\"obner Basis Theory. https://arxiv.org/abs/2201.03167

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