Moduli of real (res. quaternionic) L-connections

Abstract

We have studied irreducible real (respectively, quaternionic) Lie algebroid connections and prove that the Gauge theoretic moduli space has Hausdorff Hilbert manifold structure. This work generalises some known results about simple semi-connections for complex vector bundle on compact complex manifold in real algebraic geometry.

This is initial preprint. Any comments are most welcome