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Paper IPM / M / 16499  


Abstract:  
We develop the notion of multiloop algebras and study their derivations algebras.
Multiloop algebras are natural generalizations of loop algebras and are determined by n com
muting finite order automorphisms and a Laurent polynomials in n variables as the coordinate
algebra. In this article, we introduce extended multiloop algebras by extending the finite number
of automorphisms to a family (possibly infinitely many) of automorphisms and also using coordi
nate algebras in a family (possibly infinitely many) of variables. Also, we develop a result of the
derivations algebra of the fixed point algebra of the tensor product of two algebras with respect
to the tensor product of two finite order automorphisms. Indeed, we prove this theorem for a
family (possibly infinitely many) of automorphisms instead of one automorphism. Consequently,
we specify the derivations algebras of some extended multiloop algebras.
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