Cohomology of hemistrict Lie 2-algebras

Abstract

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-algebra $L$ and the cohomology of the semistrict Lie 2-algebra obtained from skew-symmetrization of $L$ are isomorphic to the Chevalley-Eilenberg cohomology of the induced Lie algebra $L_{\mathrm{Lie}}$.

arXiv comment22 pages

References in corpus (8)

• Leibniz 2-algebras and twisted Courant algebroids
• Courant-Dorfman algebras and their cohomology
• Lie 2-bialgebras
• Integration of Lie 2-algebras and their morphisms
• Deformations of Lie 2-algebras
• Weak Lie 2-bialgebra
• Shifted derived Poisson manifolds associated with Lie pairs
• Kapranov's construction of sh Leibniz algebras

Cited by in corpus (1)

• The standard cohomology of regular Courant algebroids