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Paper   IPM / M / 8288
School of Mathematics
  Title:   Derivations of multi-loop algebras
  Author(s):  S. Azam
  Status:   Published
  Journal: Forum Math.
  Vol.:  19
  Year:  2007
  Pages:   1029–1045
  Supported by:  IPM
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.

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