Abstract
Extensions of crossed modules in Lie algebras with abelian kernel are studied, particularly backward and forward induced extensions and related properties. The set Opext((U, Q, ɛ), (R, K, ∂)) of congruence classes of extensions of (R, K, ∂) by (U, Q, ɛ) is endowed with a K-vector space structure. This K-vector space appears in a five-term natural and exact sequence associated with an extension of crossed modules.
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