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Injective modules over down-up algebras
(Cambridge University Press, 2010) Carvalho, Paula A.A.B.; Pusat, Dilek; Lomp, Christian; Pusat, Dilek; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

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