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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.

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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