Hopf down-up algebras.

DOI10.1016/S0021-8693(03)00032-2zbMath1053.16028OpenAlexW2092477156MaRDI QIDQ1810551

Ellen E. Kirkman, Ian M. Musson

Publication date: 9 June 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(03)00032-2

zbMATH Keywords

Hopf algebrasdown-up algebras

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Universal enveloping algebras of Lie algebras (16S30) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (7)

Quantum generalized Heisenberg algebras and their representations ⋮ On category \(\mathcal O\) over triangular generalized Weyl algebras. ⋮ Down-up algebras at roots of unity ⋮ Calabi–Yau properties of nontrivial Noetherian DG down-up algebras ⋮ Hopf structures on ambiskew polynomial rings. ⋮ Down–up algebras over a polynomial base ring 𝕂[t₁,…,t_n] ⋮ Two-Parameter Analogs of the Heisenberg Enveloping Algebra

Cites Work

• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Down-up algebras
• Centers of down-up algebras
• Homological aspects of Noetherian PI Hopf algebras and irreducible modules of maximal dimension
• Down-up algebras and their representation theory
• Down-up algebras and ambiskew polynomial rings
• Noetherian down-up algebras
• Isomorphism problems and groups of automorphisms for generalized Weyl algebras
• CENTERS OF DOWN-UP ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC
• A Hopf structure for down-up algebras
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