Abstract
Abstract We introduce Lie–Nijenhuis bialgebroids as Lie bialgebroids endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson–Nijenhuis (PN) groupoids, and key examples include PN manifolds, holomorphic Lie bialgebroids and flat Lie bialgebra bundles. To achieve our goal we develop a theory of ‘generalized derivations’ and their duality, extending the well-established theory of derivations on vector bundles.
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