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math.DG2023
The Connection Algebra of Reductive Homogeneous Spaces
Jonatan Stava
Consider the smooth sections of the tangent bundle of a reductive homogeneous space. This is a vector space over the field of real numbers. The canonical connection acts as a linea…
math.DG2023
Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces
Hans Munthe-Kaas, Jonatan Stava
Associated to a symmetric space there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth se…
math.DG2023
Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion
Erlend Grong, Hans Z. Munthe-Kaas, Jonatan Stava
For a general affine connection with parallel torsion and curvature, we show that a post-Lie algebra structure exists on its space of vector fields, generalizing previous results f…