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Monogenic differential forms. (English) Zbl 0765.30032
The authors deal with the definition of monogenic differential forms with values in the Clifford algebra over \(\mathbb{R}^m\) (or in a convenient spinor space). The definition given by the first author [Trans. Am. Math. Soc. 326, 613–632 (1991; Zbl 0736.30034)] is refined to fulfill the following requirements: Invariance with respect to the \(\mathrm{Spin}(m)\) group; the homology of the underlying domain should coincide with that defined by the outer differentiation \(d\) between the spaces of monogenic \(k\)-forms; there should exist a Cauchy theorem. Such a notion is described – without proofs – by splitting the space of \(k\)-forms in a suitable way and defining monogenic forms as the kernel of the respective splitting of \(d\). This leads to the desired properties.

MSC:
30G35 Functions of hypercomplex variables and generalized variables
15A66 Clifford algebras, spinors
53C27 Spin and Spin\({}^c\) geometry
53C65 Integral geometry
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