Mathematics – Rings and Algebras
Scientific paper
2008-07-13
J. Algebra 323 no.8 (2010):2103-2129
Mathematics
Rings and Algebras
25 pages
Scientific paper
It is known that a multiloop Lie algebra, which constructed using multiloop realization, can be a Lie torus if the given multiloop Lie algebra satisfies several conditions, and it is also known that a family of extended affine Lie algebras (EALAs) are obtained from a Lie torus. In many cases, however, even if a given multiloop Lie algebra does not satisfy these conditions, we can also construct a family of EALAs from it. In this paper, we study this construction, and prove that two families of EALAs constructed from two multiloop Lie algebras are coincide up to isomorphisms as EALAs if and only if two multiloop Lie algebras are "support-isomorphic". Also, we give a necessary and sufficient condition for two multiloop Lie algebras to be support-isomorphic.
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