Hodge structures and Weierstrass \(\sigma \)-function (Q715637)

In this short note, the authors give other characterisations of the datum of a (real) Hodge structure on a finite dimensional (real) vector space. In particular, a Hodge structure can be described in terms of a single endomorphism which has to be annihilated by the Weierstrass \(\sigma\)-function associated with the lattice generated by \(\omega_1=1+i\) and \(\omega_2=1-i\).