Okubo algebras in characteristic 3 and valuations
Speaker:
Melanie Raczek, l'Université de Louvain
Date and Time:
Tuesday, May 14, 2013 - 5:15pm
Location:
Fields Institute, Room 230
Abstract:
Okubo algebras are forms of pseudo-octonion algebras, i.e. octonion algebras with a twisted product. An Okubo algebra in characteristic different from 3 and without nonzero idempotents is described as a subspace of a degree 3 central division algebra endowed with the Okubo product. Given an Okubo algebra S in characteristic 0 contained in a division algebra D which is endowed with a valuation with residue characteristic 3, I prove that the residue of S is an Okubo algebra (in characteristic 3) if and only if the residue division algebra has dimension 9 over the ground field and the height of D is maximal. Moreover Okubo algebras in characteristic 3 are always the residue of some Okubo algebra in characteristic 0.