35 citations · 131 across the 24 of their papers we have counts for
25 papers
Omni-representations of Leibniz algebras
Zhangju Liu, Yunhe Sheng
In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space as a Leibniz algebra homomorphism from $\g$ to the omni-Lie a…
The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid
Zhuo Chen, Honglei Lang, Zhangju Liu
Berwick-Evens and Lerman recently showed that the category of vector fields on a geometric stack has the structure of a Lie -algebra. Motivated by this work, we present a constr…
Multiplicative forms on Poisson groupoids
Zhuo Chen, Honglei Lang, Zhangju Liu
Given a Lie groupoid over , the tangent Lie algebroid of , and the anchor map, we provide a formula that decomposes an arbitr…
A review of Lie 2-algebras
Honglei Lang, Zhangju Liu
We first recall two equivalent definitions of Lie -algebras, categorification of Lie algebras and -term -algebras. Then we present four different kinds of Lie -a…
The Atiyah class of generalized holomorphic vector bundles
Honglei Lang, Xiao Jia, Zhangju Liu
We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bu…
Cohomology of hemistrict Lie 2-algebras
Xiongwei Cai, Zhangju Liu, Maosong Xiang
We study representations of hemistrict Lie 2-algebras and give a functorial construction of their cohomology. We prove that both the cohomology of an injective hemistrict Lie 2-alg…