Specht property for the 2 -graded identities of B m
Abstract
Let
K
be a field of characteristic zero and
V
a vector space of dimension
m>1
with a nondegenerate symmetric bilinear form
f:V×V→K
. The Jordan algebra
B
m
=K⊕V
of the form
f
is a superalgebra with this decomposition. We prove that the ideal of all the
2
-graded identities of
B
m
satisfies the Specht property and we compute the
2
-graded cocharacter sequence of
B
m
.