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Given a G-structure with connection satisfying a regularity assumption we associate to it a classifying Lie algebroid. This algebroid contains all the information about the equivalence problem and is an example of a G-structure Lie algebroid. We discuss the properties of this algebroid, the G-structure groupoids integrating it and the relationship with Cartans realization problem.
We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartans realization problem that applies to both the local and the glob
We show that the compact quotient $Gammabackslashmathrm{G}$ of a seven-dimensional simply connected Lie group $mathrm{G}$ by a co-compact discrete subgroup $Gammasubsetmathrm{G}$ does not admit any exact $mathrm{G}_2$-structure which is induced by a left-invariant one on $mathrm{G}$.
We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed G$_2$-structures, up t
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions
In this paper, we study the analytic continuation to complex time of the Hamiltonian flow of certain $Gtimes T$-invariant functions on the cotangent bundle of a compact connected Lie group $G$ with maximal torus $T$. Namely, we will take the Hamilton