Graded Polynomial Identities of the Jordan Superalgebra of a Bilinear Form Original Research Article

LetWsp, 2q=W0(p)circled plusW1(2q)be a direct sum of two vector spaces of dimensionpand 2q, respectively, over a fieldkof characteristic zero,p=2, 3,…,∞;q=1, 2,…,∞; and let left angle bracketx, yright-pointing angle bracket be a nondegenerate bilinear form onWsp, 2qwhich is symmetric onW0(p)and skew-symmetric onW1(2q)and such that left angle bracketW0(p), W1(2q)right-pointing angle bracket=left angle bracketW1(2q), W0(p)right-pointing angle bracket=0. Then the vector spaceBsp, 2q=kcircled plusWsp, 2qequipped with the product (α+v)(β+u)=(αβ+left angle bracketv, uright-pointing angle bracket)+(αu+βv), α, βset membership, variantk,v,uset membership, variantWsp, 2q, is a simple Jordan superalgebra, withk+W0(p)as its even component andW1(2q)as the odd one. In this paper explicit finite bases for graded polynomial identities of the series of Jordan superalgebrasBsp, 2q,p=2, 3,…,∞;q=1, 2,…,∞; are found.