Skip to main content
Log in

SO(m)-invariant differential operators on Clifford algebra-valued functions

  • Part III. Invited Papers Dedicated To David Hestenes
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In this paper we consider the algebra of differential operators with polynomial coefficients acting on Clifford algebra-valued functions from both sides. We characterize the subalgebra of SO(m)-invariant differential operators, which itself contains the subalgebra of GL(m)-invariant differential operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. F. Brackx, R. Delanghe, and F. Sommen,Clifford Analysis (Research Notes in Math.76) (Pitman, London, 1982).

    Google Scholar 

  2. C. Chevalley,The algebraic theory of spinors (Columbia University Press, New York, 1954).

    Google Scholar 

  3. R. Delanghe, F. Sommen, and V. Souček, “Clifford Algebra and Spinor-valued functions: a function theory for the Dirac-operator” (Mathematics and Its Applications53) (Kluwer Academic, Dordrecht, 1992).

    Google Scholar 

  4. B. Goldschmidt, “Verallgemeinerte analytische Vektore inR n,” Ph.D. Thesis, Halle, 1980.

  5. D. Hestenes and G. Sobczyk, “Clifford Algebra to Geometric Calculus” (Reidel, Dordrecht, 1985).

    Google Scholar 

  6. D. Hestenes, “The design of linear algebra and geometry,”Acta Appl. Math. 23, 65–93 (1991).

    Google Scholar 

  7. P. Lounesto, “Spinor valued regular functions in hypercomplex analysis,” Ph.D. Thesis, Helsinki, 1979.

  8. I. R. Porteous, “Topological Geometry,” 2nd edn. (Cambridge University Press, Cambridge, 1981).

    Google Scholar 

  9. F. Sommen and N. Van Acker, “Monogenic differential operators,”Results in Mathematics 22, 781–798 (1992).

    Google Scholar 

  10. N. Van Acker, “Clifford-differentiaaloperatoren en randwaardentheorie van de nuloplossingen ervan op de sfeer en de Lie-sfeer,” Ph.D. Thesis, Gent, 1992.

  11. C. Doran, D. Hestenes, F. Sommen, and N. Van Acker, “Lie groups as Spin groups,”Journal of Mathematical Physics 34(8), 3642–3669 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to D. O. Hestenes on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sommen, F., Van Acker, N. SO(m)-invariant differential operators on Clifford algebra-valued functions. Found Phys 23, 1491–1519 (1993). https://doi.org/10.1007/BF01243943

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01243943

Keywords

Navigation