ABSTRACT
Jacobian variety The Picard variety of a smooth, irreducible, projective curve. See Picard variety.
Jacobi identity The identity (x · y) · z+ (y · z) · x + (z · x) · y = 0 satisfied by any Lie algebra. For example, if A is any associative algebra, and [x, y] denotes the commutator, [x, y] = xy−yx, then the commutator satisfies the Jacobi identity [[x, y], z]+[[y, z], x]+[[z, x], y] = 0. See Lie algebra.
