The work extends non-abelian Hodge theory to transitive Lie algebroids, constructs semiprojective moduli spaces via GIT and Tannakian formalism, and derives a motivic description of their smooth loci in the Grothendieck ring.
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Lie algebroid Connections, Moduli of $\mathcal{L}$--twisted Principal Objects and motives
The work extends non-abelian Hodge theory to transitive Lie algebroids, constructs semiprojective moduli spaces via GIT and Tannakian formalism, and derives a motivic description of their smooth loci in the Grothendieck ring.