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Journal of Mathematical Physics / Volume 23 / Issue 1

J. Math. Phys. 23, 1 (1982); http://dx.doi.org/10.1063/1.525192 (7 pages)

On the classification of Clifford algebras and their relation to spinors in n dimensions

Nikos Salingaros

Mathematics Department, University of Iowa, Iowa City, Iowa 52242

A classification of all the Clifford algebras is given in terms of Kronecker products of the quaternion and dihedral groups. The relationship to spinors in n dimensions is explicitly determined. We show that the real Clifford algebra in Minkowski spacetime is distinct from both the algebra of Dirac matrices and the algebra of Majorana matrices, and cannot be realized by the spinor framework. The matrix representations of Clifford algebras are discussed, and are utilized to give a classification of the real forms of Lie algebras. We are thus able to relate Clifford, Lie, and spinor algebras in an intrinsic geometrical setting.

ERRATUM

  1. Erratum: On the classification of Clifford algebras and their relation to spinors in n dimensions [J. Math. Phys. 23, 1 (1982)]
    Nikos Salingaros
    J. Math. Phys. 23, 1231 (1982)JMAPAQ000023000006001231000001

KEYWORDS and PACS

Keywords

CLIFFORD ALGEBRA, CLASSIFICATION, SYMMETRY GROUPS, SPINORS, MINKOWSKI SPACE, MATRICES

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.525192

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    N. Salingaros, J. Math. Phys. 22, 226 (1981JMAPAQ000022000002000226000001).

    A. Pais, J. Math. Phys. 3, 1135 (1962JMAPAQ000003000006001135000001).

    N. Salingaros, “Algebras With Three Anticommuting Elements. II,” J. Math. Phys. 22, 2096 (1981JMAPAQ000022000010002096000001).

    Y. Ilamed and N. Salingaros, “Algebras With Three Anticommuting Elements. I,” J. Math. Phys. 22, 2091 (1981JMAPAQ000022000010002091000001).

    N. Salingaros and M. Dresden, Phys. Rev. Lett. 43, 1 (1979).

    N. Salingaros, “Electromagnetism and the Holomorphic Properties of Spacetime,” J. Math. Phys. 22, 1919 (1981JMAPAQ000022000009001919000001).


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