S 7 and. . .

Abstract

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moodylike algebra. Covariance properties and tensorial composition of spinors under S 7 are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given. published in Commun.Math.Phys. 167 (1995) 373. ? e-mail [email protected] y e-mail [email protected] M. Cederwall and C.R. Preitschopf, "S 7 and c S 7 " 1. Preliminaries. This paper is devoted to an investigation of the seven-sphere as a manifold equipped with group-like multiplication, and to its extension to a Kac-Moody-like algebra. As is well known, the seven-..