English

L-infinity Formality check for the Hochschild Complex of Certain Universal Enveloping Algebras

Quantum Algebra 2018-07-10 v1

Abstract

We study the L-infinity-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 generated by a vector space of dimension at least 2. We show that for these examples formality in Kontsevich's sense does NOT hold, although some of them allow unconditioned deformability. We compute the L-infinity-structure on the cohomology given by homotopy transfer in certain cases.

Keywords

Cite

@article{arxiv.1807.03086,
  title  = {L-infinity Formality check for the Hochschild Complex of Certain Universal Enveloping Algebras},
  author = {Martin Bordemann and Olivier Elchinger and Simone Gutt and Abdenacer Makhlouf},
  journal= {arXiv preprint arXiv:1807.03086},
  year   = {2018}
}

Comments

48 pages