Abstract
The structure of a complex Clifford algebra is studied by direct sum decompositions into eigenspaces of specific linear operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brackx F., Bureš J., De Schepper H., Eelbode D., Sommen F., Souček V.: Fundaments of Hermitean Clifford Analysis. Part I: Complex structure. Compl. Anal. Oper. Theory 1(3), 341–365 (2007)
Brackx F., Bureš J., De Schepper H., Eelbode D., Sommen F., Souček V.: Fundaments of Hermitean Clifford Analysis. Part II: Splitting of h-monogenic equations. Complex Var. Elliptic Eq. 52(10-11), 1063–1079 (2007)
Brackx F., De Knock B., De Schepper H.: A matrix Hilbert transform in Hermitean Clifford analysis. J. Math. Anal. Appl. 344, 1068–1078 (2008)
Brackx F., De Knock B., De Schepper H., Sommen F.: On Cauchy and Martinelli–Bochner integral formulae in Hermitean Clifford analysis. Bull. Braz. Math. Soc. New Series 40(3), 395–416 (2009)
Brackx F., Delanghe R., Sommen F.: Clifford Analysis. Pitman Publishers, Boston-London-Melbourne (1982)
Brackx F., Delanghe R., Sommen F.: Differential forms and/or multivector functions. Cubo 7(2), 139–169 (2005)
Brackx F., De Schepper H., Eelbode D., Souček V.: The Howe dual pair in Hermitean Clifford analysis. Rev. Mat. Iberoamericana 26(2), 449–479 (2010)
F. Brackx, H. De Schepper, R. Lávička and V. Souček, Dirac and Moisil- Téodorescu systems in Hermitean Clifford Analysis. (To appear).
Brackx F., De Schepper H., Sommen F.: A theoretical framework for wavelet analysis in a Hermitean Clifford setting. Comm. Pure Appl. Anal. 6(3), 549–567 (2007)
Brackx F., De Schepper H., Sommen F.: The Hermitean Clifford analysis toolbox. Adv. appl. Clifford alg. 18(3-4), 451–487 (2008)
F. Brackx, H. De Schepper and V. Souček, Differential Forms versus Multivector Functions in Hermitean Clifford Analysis. To appear in Cubo.
Damiano A., Eelbode D., Sabadini I.: Invariant syzygies for the Hermitian Dirac operator. Math. Zeitschrift 262, 929–945 (2009)
R. Delanghe, R. Lávička and V. Souček, On polynomial solutions of generalized Moisil-Théodoresco systems and Hodge-de Rham systems. (To appear).
R. Delanghe, R. Lávička and V. Souček, The Fischer decomposition for Hodgede Rham systems in Euclidean spaces. (To appear).
Delanghe R., Sommen F., Souček V.: Clifford Algebra and Spinor-Valued Functions. Kluwer Academic Publishers, Dordrecht - Boston - London (1992)
Gilbert J., Murray M.: Clifford Algebras and Dirac Operators in Harmonic Analysis. Cambridge University Press, Cambridge (1991)
Gürlebeck K., Habetha K., Gürlebeck W.: Holomorphic Functions in the Plane and n-dimensional Space. Birkhäuser Verlag, Basel (2008)
R. Lavicka, On the structure of monogenic multivector valued polynomials. In: T.E. Tsimos, G. Psihoyios, Ch. Tsitouras (eds.). Proceedings of ICNAAM 2009, AIP Conference Proceedings 1168, 793-796.
R. Lavicka, The Fischer decomposition for the H-action and its applications. Submitted for Proceedings of ISAAC 2009, London.
Michelsohn M.L.: Clifford and Spinor Cohomology of Kähler Manifolds. American Journal of Mathematics 102(6), 1083–1146 (1980)
Moroianu A.: Lectures on Kähler geometry. London Mathematical Society Student Texts 69. Cambridge University Press, Cambridge (2007)
Porteous I.R.: Topological Geometry. Van Nostrand Reinhold Company, London - New York - Toronto - Melbourne (1969)
Sabadini I., Sommen F.: Hermitian Clifford analysis and resolutions. Math. Meth. Appl. Sci. 25(16–18), 1395–1414 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brackx, F., De Schepper, H. & Souček, V. On the Structure of Complex Clifford Algebra. Adv. Appl. Clifford Algebras 21, 477–492 (2011). https://doi.org/10.1007/s00006-010-0270-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00006-010-0270-4