Clifford algebras and spinors. 2nd ed.

*(English)*Zbl 0973.15022
London Mathematical Society Lecture Note Series. 286. Cambridge: Cambridge University Press. ix, 338 p. (2001).

The second edition of ‘Clifford algebras and spinors’, reprinted already two times in the first edition, is welcome in the Clifford algebra community where it has already taken its prominent place on the book shelf but most likely much more by ‘newcomers’ joining the dynamical growing exciting field. Even titulated as ‘bible’, by some colleagues, this book cannot be underestimated in its current influence as it opened the ‘seven seals’ of Clifford algebras to a wide range of persons.

The content, described in the review of the first edition (1997; Zbl 0887.15029) has not changed but was slightly extended. Small typographical errors have been corrected and a new chapter on octonions and triality, already announced in the first edition, has been added. This chapter explores the octonions and the remarkable fact of triality intimately connected to exceptional Lie groups. A further chapter on the history of Clifford algebras which summarises and completes the remarks spread out already over the book is also new.

The content, described in the review of the first edition (1997; Zbl 0887.15029) has not changed but was slightly extended. Small typographical errors have been corrected and a new chapter on octonions and triality, already announced in the first edition, has been added. This chapter explores the octonions and the remarkable fact of triality intimately connected to exceptional Lie groups. A further chapter on the history of Clifford algebras which summarises and completes the remarks spread out already over the book is also new.

Reviewer: B.Fauser (Tübingen)

##### MSC:

15A66 | Clifford algebras, spinors |

15-02 | Research exposition (monographs, survey articles) pertaining to linear algebra |

30G35 | Functions of hypercomplex variables and generalized variables |

15A90 | Applications of matrix theory to physics (MSC2000) |

15A75 | Exterior algebra, Grassmann algebras |

11E81 | Algebraic theory of quadratic forms; Witt groups and rings |

83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |

81R25 | Spinor and twistor methods applied to problems in quantum theory |

15-03 | History of linear algebra |