S-7 AND (S-7)OVER-CAP

We investigate the seven-sphere as a group-like manifold and its exten sion to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under S-7 are defined. The relation to Malcev a lgebras is established. The consequences for octonionic projective spa ces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coeffici ents) up to redefinitions of the currents. Nilpotency of the BRST oper ator is consistent with one particular expression in the class of (fie ld-dependent) anomalies. A Sugawara construction is given.