The Connection Algebra of Reductive Homogeneous Spaces

Abstract

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 linear binary operator on this vector space, making it an algebra. If we include another binary operator defined as the negative of the torsion, the resulting algebraic structure is a post-Lie-Yamaguti algebra. This structure is closely related to Lie-Yamaguti algebras.

24 pages

References in corpus (10)

• Homology of generalized partition posets
• Two interacting Hopf algebras of trees
• On post-Lie algebras, Lie--Butcher series and moving frames
• Pre-Lie algebras and the rooted trees operad
• On the Lie enveloping algebra of a post-Lie algebra
• Monomial bases for free pre-Lie algebras
• Algebraic aspects of connections: from torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials
• Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion
• Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces
• A Berger-type theorem for metric connections with skew-symmetric torsion