Abstract
In this note I discuss some properties and (anti)-commutation relations of Clifford differentiation operators on ℝ n which are geometrical invariants. The results are a happy and accidental combination of earlier work on spherical vector fields [G] and inspiration drawn from Van Acker’s PhD-Thesis [A] on Clifford differential operators.
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References
Acker, N. van, Clifford differentiaaloperatoren en randwaardetheorie van de nuloplossingen ervan op de sfeer en de Lie-sfeer. Proefschrift, Rijksuniversiteit Gent, 1991–1992.
[] Chisholm, J.S.R. and R.S. Farwell, CLifford approach to metric manifolds. Proc. Winterschool on Geometry and Physics. SRNI, 6–13 January, 1990, pp. 123–133.
Graaf, J. de, Skew Hermitean Representations of Lie Algebras of Vector Fields on the Unit-Sphere. Mitteilungen der Math. Gesellschaft Hamburg. Band XII, Heft 3, 1991, 705–711.
Schouten, J.A., Tensor analysis for physicists. Dover Edition, New York, 1989.
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© 1993 Kluwer Academic Publishers
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De Graaf, J. (1993). Note on the Use of Spherical Vectorfields in Clifford Analysis. In: Brackx, F., Delanghe, R., Serras, H. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2006-7_11
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DOI: https://doi.org/10.1007/978-94-011-2006-7_11
Publisher Name: Springer, Dordrecht
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