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L∞-formality check for the Hochschild complex of certain universal enveloping algebras

par Bordemann, Martin ;Elchinger, Olivier;Gutt, Simone ;Makhlouf, Abdenacer
Référence Journal of geometry and physics, 187, 104789
Publication Publié, 2023-05

Article révisé par les pairs

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Résumé :

We study the L∞-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more detail so(3)), and free Lie algebras. We show that for these examples formality in Kontsevich's sense does NOT hold, but we compute the L∞ structure on the cohomology given by homotopy transfer in certain cases.