Abstract
In this paper, the composition problem of hermitian forms and quadratic forms is completely solved, which is related to the classical Hurwitz problem of composition of quadratic forms and the recent results due to J. Ławrynowicz, J. Rembielinski, and P. Yiu. This result also determines the signatures of pseudo-euclidean spaces which admit generalized Dirac operators. Our main conclusion is stated in Theorem 3; in fact it is a more explicit version of some results of Ławrynowicz and Rembielinski.
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