  In this article we give a Galois-theoretic characterization of the canonical
theta structure. The Galois property of the canonical theta structure
translates into certain $p$-adic theta relations which are satisfied by the
canonical theta null point of the canonical lift. As an application we give a
purely algebraic proof of some 2-adic theta identities which describe the set
of theta null points of the canonical lifts of ordinary abelian varieties in
characteristic 2. The latter theta relations are suitable for explicit
canonical lifting.
