Abstract
It is shown that the previously known N=3 and N=4 superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the latter case, by a contraction which depends on the central term, we obtain a new N=4 superconformal algebra which contains an SU (2)× U (1)4 Kac-Moody subalgebra and has nonzero central extension.
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