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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 < ottmar.loos@uibk.ac.at >