Budinich, Paolo; Trautman, Andrzej The spinoral chessboard. (English) Zbl 0653.15022 Trieste Notes in Physics. Berlin etc.: Springer-Verlag. viii, 128 p. DM 45.00 (1988). The book under review represents a first step towards the study of spinors and simple spinors in higher-dimensional real pseudo-Euclidean spaces that are of possible interest to physicists. The authors give all necessary mathematical notions including vector spaces with real and complex structure, inner products in vector spaces, algebras and their representations. Among useful techniques presented are Clifford algebras associated with real vector spaces with scalar products (in particular their representations, grading and periodicities), general properties of spinor spaces, bilinear forms and conjugations. As the authors write in the preface of the book special attention is paid to research work in theoretical physics, where often, besides theorems and propositions, algorithms are required for explicit calculations. Reviewer: N.I.Osetinski Cited in 22 Documents MSC: 15A66 Clifford algebras, spinors 15-02 Research exposition (monographs, survey articles) pertaining to linear algebra 53C27 Spin and Spin\({}^c\) geometry Keywords:textbook; spinors; pseudo-Euclidean spaces; Clifford algebras; representations; grading; periodicities; bilinear forms; conjugations PDFBibTeX XMLCite \textit{P. Budinich} and \textit{A. Trautman}, The spinoral chessboard. Berlin etc.: Springer-Verlag (1988; Zbl 0653.15022)