EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 12, No. 2, pp. 515--527 (2002)

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Extended Affine Root Systems

Saeid Azam

Saeid Azam
Department of Mathematics
University of Isfahan
Isfahan, Iran
P.O.Box 81745
Institute for Studies in Theoretical Physics and Mathematics (IPM)

Abstract: There are two notions of the extended affine root systems in the literature which both are introduced axiomatically. One, extended affine root system (SAERS for short), consists only of nonisotropic roots, while the other, extended affine root system (EARS for short), contains certain isotropic roots too. We show that there is a one to one correspondence between (reduced) SEARSs and EARSs. Namely the set of nonisotropic roots of any EARS is a (reduced) SEARS, and conversely, there is a unique way of adding certain isotropic elements to a SEARS to get an EARS. (It is known that some of extended affine root systems are not the root system of any extended affine Lie algebra.) Every article should have an abstract.

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Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.

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