An introduction to the spinorial chessboard
With the applications of higher-dimensional spinors to physics in mind, the authors give an account of the real Clifford algebras. Let Cl(k,\(\ell)\) denote the Clifford algebra associated with a real scalar product of signature (k,\(\ell)\). The spinorial chessboard of the title is made up of the 64 such algebras with \(0\leq k,\ell \leq 7\). Certain periodicities relate the properties of the general Cl(k,\(\ell)\) to those on the chessboard. For example, its type and the kind of symmetry of its invariant bilinear form depend only on the respective values of k-\(\ell\) and \(k+\ell\) modulo 8. The inductive construction of a set of Dirac matrices, and of other related matrices, are discussed in some detail. The present article is intended as an introduction to a more detailed account of the spinorial chessboard.
scientific article; zbMATH DE number 4073198
scientific article