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

In this paper, we classify the equivalence classes of non-abelian extensions of a Lie H-pseudoalgebra L by another Lie H-pseudoalgebra Min terms of the non-abelian cohomology group H2nab(L, M). We also show that the group H2nab(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. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.