Cubic and symmetric compositions over rings

Consider generalized symmetric compositions over a ring k on the one hand, and unital algebras with multiplicative cubic forms on the other. Given a primitive sixth root of unity in k, we construct functors between these categories which are equivalences if 3 is a unit in k. This extends to arbitrary base rings, and with new proofs, results of Elduque and Myung on non-degenerate symmetric compositions and separable alternative algebras of degree 3 over fields.

The original publication is available at, DOI: 10.1007/s00229-007-0111-5 and has appeared in manuscr. math. 124 (2007), 195--236.

(Corrected version 14 Oct 2007)

Ottmar Loos < >