Non-abelian cohomology of Lie H-pseudoalgebras and inducibility of automorphisms

Abstract

In this paper, we classify the equivalence classes of non-abelian extensions of a Lie H-pseudoalgebra L by another Lie H-pseudoalgebra M in terms of the non-abelian cohomology group $H_{nab}^2(L,M)$. We also show that the group $H_{nab}^2(L,M)$ can be realized as the Deligne groupoid of a suitable differential graded Lie algebra. Finally, we consider the inducibility of a pair of Lie H-pseudoalgebra automorphisms in a given non-abelian extension. We show that the corresponding obstruction can be realized as the image of a suitable Wells map in the context.