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

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

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arXiv · 2204.01352

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

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

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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.

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Clay J. Grewcoe, Larisa Jonke, Toni Kodzoman, George Manolakos. 2022-04-04. From Hopf algebra to braided $L_\infty$-algebra. https://arxiv.org/abs/2204.01352

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