The relationship between finite groups and Clifford algebras.

*(English)*Zbl 0552.20008As well known, Clifford algebras are of a great importance in studies of space-time symmetries and their extensions to a unified description of gauge fields. Usually Clifford algebras are realized in terms of a specific set of representation matrices. In the paper under review properties of Clifford algebras are studied in another way, namely, in terms of the corresponding finite groups. This approach generalizes the usual procedure of deriving properties of Clifford algebras by means of representation matrices. The author constructs five types of groups which are determined by Clifford algebras in an arbitrary dimension and presents a table which provides an identification of any Clifford algebra arising in physics via a simple computation of its order structure.

Reviewer: E.Kryachko

##### MSC:

20C35 | Applications of group representations to physics and other areas of science |

15A66 | Clifford algebras, spinors |

81T60 | Supersymmetric field theories in quantum mechanics |

81T08 | Constructive quantum field theory |

81T17 | Renormalization group methods applied to problems in quantum field theory |

##### Keywords:

Clifford algebras; space-time symmetries; gauge fields; representation matrices; finite groups
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DOI

##### References:

[1] | DOI: 10.1063/1.524893 · Zbl 0459.15017 · doi:10.1063/1.524893 |

[2] | DOI: 10.1063/1.525192 · Zbl 0481.15013 · doi:10.1063/1.525192 |

[3] | DOI: 10.2307/2371218 · Zbl 0011.24401 · doi:10.2307/2371218 |

[4] | Witt E., J. Reine Angew. Math. 176 pp 31– (1936) |

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