Symmetries of WDVV equations

We say that a function F (τ) obeys WDVV equations, if for a given invertible symmetric matrix η and all τ ∈ T ⊂ R, the expressions c α β γ(τ) = η cλβγ(τ) = η∂λ∂β∂γF can be considered as structure constants of commutative associative algebra; the matrix ηαβ inverse to η αβ determines an invariant scalar product on this algebra. A function x(z, τ) obeying ∂α∂βx (z, τ) = zc ε α β∂εx (z, τ) is called a calibration of a solution of WDVV equations. We show that there exists an infinitedimensional group acting on the space of calibrated solutions of WDVV equations (in different form such a group was constructed in [2]). We describe the action of Lie algebra of this group. [email protected] [email protected] [email protected]