Down–up algebras over a polynomial base ring 𝕂[t1,…,tn]

DOI10.1142/S0219498816500249zbMath1395.16030MaRDI QIDQ2788563

Xin Tang

Publication date: 19 February 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

global dimensionKrull dimensiondown-up algebrasalgebra automorphism

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Automorphisms and endomorphisms (16W20) Growth rate, Gelfand-Kirillov dimension (16P90) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Cites Work

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• Classification of factorial generalized down-up algebras.
• The diamond lemma for ring theory
• Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients
• Down-up algebras
• Centers of down-up algebras
• Irreducible finite-dimensional modules of prime characteristic down-up algebras.
• Down-up algebras and their representation theory
• Down-up algebras and ambiskew polynomial rings
• Hopf down-up algebras.
• Basic properties of generalized down-up algebras.
• Fixed subrings of Noetherian graded regular rings.
• Primitive Ideals of Noetherian Down-Up Algebras
• Down-Up Algebras From Trees
• Automorphisms of Generalized Down-Up Algebras
• Noetherian down-up algebras
• Primitivity of Noetherian Down-Up Algebras
• Isomorphism problems and groups of automorphisms for generalized Weyl algebras
• Non-noetherian down-up algebras
• CENTERS OF DOWN-UP ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC
• PRIMITIVE IDEALS OF NON-NOETHERIAN DOWN-UP ALGEBRAS
• Homogenized Down-Up Algebras
• Generalized Weyl algebras are tensor Krull minimal
• A Hopf structure for down-up algebras
• Down-up algebras and their representations.

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