For rings defined by monomial ideals, embedded deformations, free summands of the conormal module, and central or radical degree-2 homotopy Lie algebra elements are equivalent.
Avramov and Ragnar-Olaf Buchweitz
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The embedded deformation problem for monomial ideals
For rings defined by monomial ideals, embedded deformations, free summands of the conormal module, and central or radical degree-2 homotopy Lie algebra elements are equivalent.