Abstract
The Lipschitz semigroup is generated by all (invertible and noninvertible) Clifford vectors. We show that all solutions of the equation xy = 0 (where x, y are non-zero elements of the Lipschitz semigroup) are of the form x = av0, y = v0b where v0 is an isotropic vector (i.e., v 0 2 = 0). This problem turns out to be useful in the construction of multisoliton solutions of integrable systems of nonlinear partial differential equtions.
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