“School of Mathematics”
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| Paper IPM / M / 751 |
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| Abstract: | |
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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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