zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Clifford algebras. An introduction. (English) Zbl 1235.15025
London Mathematical Society Student Texts 78. Cambridge: Cambridge University Press (ISBN 978-1-107-42219-3/pbk; 978-1-107-09638-7/hbk). vii, 200 p. £ 23.99, $ 39.99/pbk; £ 60.00, /hbk$ 99.00/hbk (2011).

This book came to join some other very good works in the literature of Clifford algebras. It is a clear and concise introduction to Clifford algebras directed to advanced undergraduate and graduate students.

The work it divided into three major parts. The first part is concerned with the background needed to develop the theory of Clifford algebras. Some definitions and results involving the concepts of groups, vector spaces and algebras are recalled, and taking advantage to fix the notation and terminology used in the rest of the text. The second is the main part of the book, where Clifford algebras are constructed over real quadratic spaces. Real Clifford algebras have a much richer structure than the complex Clifford algebras, and this is exploited in detail. All important properties of Clifford algebras are discussed, in particular the periodicity theorems, which are key to their classification. Spinor spaces and spin groups are also discussed. The final part of the book is concerned with applications of Clifford algebras. Some important applications in Physics (as in Maxwell and Dirac equations), generalizations of complex analysis, and differential geometry, are discussed in order to call the reader’s attention and to invite him/her to go deeper in those studies, using references that are suggested at the end. The book has dozens of exercises distributed throughout the text.

In the opinion of this reviewer, the book is well written and is recommended to all those wishing to start a mathematical study of Clifford algebras.

15A66Clifford algebras, spinors
15-01Textbooks (linear algebra)
11-01Textbooks (number theory)
11E88Quadratic spaces; Clifford algebras