The Grassmann envelope of the Kac superalgebra sK10
We investigate in detail the structure of the Grassmann envelope of the
split Kac superalgebra sK10 over an arbitrary ring of scalars, verifying
that it is indeed a quadratic Jordan algebra, generically algebraic of
degree at most 9, and obtain the bizarre result that in characteristic 5
(but not otherwise) it is the Jordan algebra of a sharped cubic form.
K. McCrimmon < kmm4m@virginia.edu >