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Paper   IPM / M / 16499
School of Mathematics
Title:   Derivations of extended multi-loop algebras
Author(s):
 1 Saeid Azam 2 Gholamreza Behboodi
Status:   Published
Journal: J. Lie Theory
Vol.:  29
Year:  2019
Pages:   247-262
Supported by:  IPM
Abstract:
We develop the notion of multi-loop algebras and study their derivations algebras. Multi-loop 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 multi-loop 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 multi-loop algebras.