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Generalized Down-up Algebras Revisited from A Viewpoint of Gröbner Basis Theory

2022/01/10 by Rabigul Tuniyaz, Tuniyaz, Rabigul, Gulshadam Yunus +1
Engineering · #16W70 #16Z05 #FOS: Mathematics #Photonic and Optical Devices #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2201.03167

openalex publication_date 2022/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 λω≠ 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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