Conformal groups in geometry and spin structures
type: Item
instance of: scholarly article
title: Conformal groups in geometry and spin structures
zbMATH Open document ID: 1136.53001
author: Pierre Anglès
published in: Progress in Mathematical Physics
publication date: 2006-12-14T00:00:00Z
review text: This is a remarkable book that will be a valuable addition to the library of anyone interested in either conformal groups in geometry, or spin structures. Notwithstanding the comments of the author, and the publisher, in the opinion of the reviewer it is neither a textbook (for advanced undergraduates, or graduate students), nor is it a systematic treatise on either topic. Rather it is a goldmine of information containing essentially everything that has been written on conformal groups, and spin structures. It consists of three chapters: Classical Groups, Clifford-Algebras, Projective Quadrics, and Spin-Groups (pages 1--70); Real Conformal Spin Structures (pages 71-204); Pseudo-unitary Conformal Spin Structures (pages 205--273). There is also an adequate index of topics of nine pages, but no name index of authors cited in the text. The latter makes it a time consuming task to find references to a particular author, and is a serious defect that could have easily been remedied. The typography is excellent, and there are few typographical misprints in the equations. However, a number of the first and middle names of non-French authors, are wrong, e.g. see those of Wessel, Study, and Clifford on page xiv. On page vii, opposite an impressive portrait of Clifford, there is a quotation attributed to Hermann Weyl. While Weyl may have informally made such a comment, a similar but somewhat different one, may be found in his 1939 paper, `Invariants' (see his `Gesammelte Werke', Band III, page 681). In conclusion, despite its minor defects, the reviewer can warmly recommend the volume to prospective readers. It is a wonderful addition to the existing literature!
Mathematics Subject Classification ID: 53-01
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 5080030
zbMATH Keywords: conformal groups in geometry
zbMATH Keywords: spin structures
zbMATH Keywords: Clifford algebras
zbMATH Keywords: spinors
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5080030