Derivations of multi-loop algebras

This article is about the derivation algebra of multi-loop algebras. Multi-loop algebras are algebras obtained by a generalization of a process known as twisting by automorphisms in the theory of Kac–Moody algebras. Multi-loop algebras are used in the realization of extended affine Lie algebras. Under certain conditions on an algebra 𝒜, we determine the derivation algebra of an n-step multi-loop algebra based on 𝒜 as the semidirect product of a multi-loop algebra based on the derivation algebra of 𝒜 and the derivation algebra of the Laurent polynomials in n-variables. This in particular determines the derivation algebras of the core modulo center of (almost all) extended affine Lie algebras.