From Hopf algebra to braided $L_\infty$-algebra

Clay J. Grewcoe; Larisa Jonke; Toni Kodzoman; George Manolakos

From Hopf algebra to braided $L_\infty$-algebra

High Energy Physics - Theory 2022-08-03 v2 Mathematical Physics Differential Geometry math.MP

Authors: Clay J. Grewcoe , Larisa Jonke , Toni Kodzoman , George Manolakos

Abstract

We show that an $L_\infty$ -algebra can be extended to a graded Hopf algebra with a codifferential. Then we twist this extended $L_\infty$ -algebra with a Drinfel'd twist, simultaneously twisting its modules. Taking the $L_\infty$ -algebra as its own (Hopf) module, we obtain the recently proposed braided $L_\infty$ -algebra. The Hopf algebra morphisms are identified with the strict $L_\infty$ -morphisms, while the braided $L_\infty$ -morphisms define a more general $L_\infty$ -action of twisted $L_\infty$ -algebras.

Keywords

hopf algebras lie algebras and representations

Cite

@article{arxiv.2204.01352,
  title  = {From Hopf algebra to braided $L_\infty$-algebra},
  author = {Clay J. Grewcoe and Larisa Jonke and Toni Kodzoman and George Manolakos},
  journal= {arXiv preprint arXiv:2204.01352},
  year   = {2022}
}

Comments

to appear in the Special Issue of Universe on "Dualities and Geometry"; v2: typos in eqs.(2.8) and (3.11) fixed

From Hopf algebra to braided $L_\infty$-algebra

Abstract

Keywords

Cite

Comments

Related papers