For a field K, let R denote the Jacobson algebra K⟨X,Y | XY = 1⟩. We give an explicit construction of the injective envelope of each of the (infinitely many) simple left R-modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for R. Our approach involves realizing R up to isomorphism as the Leavitt path K-algebra of an appropriate graph T , which thereby allows us to utilize important machinery developed for that class of algebras.

Injective modules over the Jacobson algebra $Klangle X, Y | XY=1rangle $

Abrams, Gene;Mantese, Francesca;
2021-01-01

Abstract

For a field K, let R denote the Jacobson algebra K⟨X,Y | XY = 1⟩. We give an explicit construction of the injective envelope of each of the (infinitely many) simple left R-modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for R. Our approach involves realizing R up to isomorphism as the Leavitt path K-algebra of an appropriate graph T , which thereby allows us to utilize important machinery developed for that class of algebras.
2021
injective modules over Leavitt path algebras
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1023840
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