Canonical form of a pair of compatible antibrackets

In the triplectic quantization of general gauge theories, we prove a triplectic analogue of the Darboux theorem: we show that the doublet of compatible antibrackets can be brought to a weakly-canonical form provided the general triplectic axioms of Batalin et al. [Nucl. Phys. B 446 (1995) 249] are imposed in combination with some additional requirements that can be formulated in terms of marked functions of the antibrackets. The weakly-canonical antibrackets involve an obstruction to bringing them to the canonical form. We also classify the `triplecticʹ odd vectors fields compatible with the weakly-canonical antibrackets and construct the Poisson bracket associated with the antibrackets and the odd vector fields. We also formulate and investigate the consequences of the Sp(2)-covariance requirement for the antibrackets and the odd vector fields.