Realization of locally extended affine Lie algebras of type $A_1$

Document Type : Research Paper


Department of Mathematics, University of Isfahan, Isfahan, Iran, P.O.Box: 81745-163 and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746.


Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight vectors corresponding to nonisotropic roots modulo its centre. In this paper, in order to realize locally extended affine Lie algebras of type $A_1$, using the notion of Tits-Kantor-Koecher construction, we construct some Lie algebras which are isomorphic to the centerless cores of these algebras.


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