Specht property for the 2-graded identities of the Jordan algebra of a bilinear form

Abstract

ABSTRACTLet 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 Bm = K⊕V of the form f is a ℤ2-graded algebra with this decomposition. We prove that the ideal of all the ℤ2-graded identities of Bm satisfies the Specht property and we compute the ℤ2-graded cocharacter sequence of Bm.