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Published online by Cambridge University Press: 10 June 2016
In a previous paper, we studied the homogenized enveloping algebra of the Lie algebra sℓ(2,ℂ) and the homogenized Verma modules. The aim of this paper is to study the homogenization $\mathcal{O}$B of the Bernstein–Gelfand–Gelfand category $\mathcal{O}$ of sℓ(2,ℂ), and to apply the ideas developed jointly with J. Mondragón in our work on Groebner basis algebras, to give the relations between the categories $\mathcal{O}$B and $\mathcal{O}$ as well as, between the derived categories $\mathcal{D}$b($\mathcal{O}$B) and $\mathcal{D}$b($\mathcal{O}$).