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In this paper, we introduce the notion of a pre-Lie 2-algebra, which is the categorification of a pre-Lie algebra. We prove that the category of pre-Lie 2-algebras and the category of 2-term pre-Lie$_\infty$-algebras are equivalent. We classify skeletal pre-Lie 2-algebras by the third cohomology group of a pre-Lie algebra. We prove that crossed modules of pre-Lie algebras are in one-to-one correspondence with strict pre-Lie 2-algebras. O-operators on Lie 2-algebras are introduced, which can be used to construct pre-Lie 2-algebras. As an application, we give solutions of 2-graded classical Yang-Baxter equations in some semidirect product Lie 2-algebras.
@article{TAC_2019_34_a10,
author = {Yunhe Sheng},
title = {Categorification of {pre-Lie} {Algebras} and solutions of 2-graded {classical
Yang-Baxter} equations},
journal = {Theory and applications of categories},
pages = {269--294},
publisher = {mathdoc},
volume = {34},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a10/}
}
TY - JOUR AU - Yunhe Sheng TI - Categorification of pre-Lie Algebras and solutions of 2-graded classical Yang-Baxter equations JO - Theory and applications of categories PY - 2019 SP - 269 EP - 294 VL - 34 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2019_34_a10/ LA - en ID - TAC_2019_34_a10 ER -
Yunhe Sheng. Categorification of pre-Lie Algebras and solutions of 2-graded classical Yang-Baxter equations. Theory and applications of categories, Tome 34 (2019), pp. 269-294. http://geodesic.mathdoc.fr/item/TAC_2019_34_a10/