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 http://www.springerlink.com,
DOI: 10.1007/s00229-007-0111-5 and has appeared in manuscr. math. 124 (2007), 195--236.
(Corrected version 14 Oct 2007)
Ottmar Loos < email@example.com >